MATH 3600 2020-10-07 Collatz

294 days ago by calkin

def f(n): if n.is_integer()==False or n<1: return("please input a positive integer") if is_even(n): n=n/2 else: n=3*n+1 return(n) def h(n): if n.is_integer()==False or n<1: return("please input a positive integer") if n==1: return(0) count=0 a=n while a>1: a=f(a) count+=1 return(count) 
       
N=100000 hail=[] for n in srange(1, N): hail.append([n,h(n)]) 
       
champs=[] maxh=-1 for n in srange(1,N): a=h(n) if a>maxh: maxh=a champs.append(n) 
       
list_plot(champs) 
       
print(champs) 
       
[1, 2, 3, 6, 7, 9, 18, 25, 27, 54, 73, 97, 129, 171, 231, 313, 327, 649,
703, 871, 1161, 2223, 2463, 2919, 3711, 6171, 10971, 13255, 17647,
23529, 26623, 34239, 35655, 52527, 77031]
[1, 2, 3, 6, 7, 9, 18, 25, 27, 54, 73, 97, 129, 171, 231, 313, 327, 649, 703, 871, 1161, 2223, 2463, 2919, 3711, 6171, 10971, 13255, 17647, 23529, 26623, 34239, 35655, 52527, 77031]
len(champs) 
       
35
35
double_champs=[] for i in champs: if h(i)==h(i+1): double_champs.append(i) 
       
print(double_champs) 
       
[18, 54]
[18, 54]
h(25) 
       
23
23
h(31) 
       
106
106
list_plot(hail) 
       
N=10000 paired_values=[] for i in srange(N): if h(i)==h(i+1): paired_values.append(i) print(paired_values) 
       
[12, 14, 18, 20, 22, 28, 29, 34, 36, 37, 44, 45, 49, 50, 52, 54, 60, 62,
65, 66, 68, 69, 76, 78, 82, 84, 86, 92, 94, 98, 99, 100, 101, 108, 109,
114, 116, 118, 124, 125, 130, 131, 132, 133, 140, 142, 145, 146, 148,
150, 156, 157, 162, 164, 165, 172, 173, 177, 178, 180, 182, 188, 189,
193, 194, 196, 197, 204, 206, 209, 210, 212, 214, 220, 222, 226, 228,
229, 236, 237, 240, 242, 244, 246, 252, 254, 257, 258, 260, 261, 268,
270, 274, 276, 278, 284, 285, 290, 291, 292, 293, 300, 301, 305, 306,
308, 310, 314, 315, 316, 318, 322, 324, 325, 332, 334, 338, 340, 342,
348, 350, 354, 355, 356, 357, 364, 365, 368, 370, 372, 374, 380, 382,
386, 387, 388, 389, 390, 396, 398, 401, 402, 404, 406, 412, 413, 418,
419, 420, 421, 428, 429, 433, 434, 436, 438, 444, 445, 450, 452, 453,
460, 462, 466, 468, 470, 472, 473, 476, 478, 482, 484, 485, 492, 493,
498, 500, 502, 508, 509, 514, 515, 516, 517, 524, 526, 528, 530, 532,
534, 540, 541, 546, 548, 549, 556, 557, 561, 562, 564, 566, 572, 574,
577, 578, 580, 581, 586, 587, 588, 590, 593, 594, 596, 598, 604, 606,
610, 611, 612, 613, 620, 621, 626, 628, 629, 630, 631, 636, 637, 642,
644, 645, 652, 654, 657, 658, 660, 662, 668, 669, 674, 676, 677, 684,
685, 689, 690, 692, 694, 700, 701, 706, 708, 709, 716, 718, 721, 722,
724, 726, 732, 734, 738, 740, 741, 747, 748, 749, 754, 756, 758, 764,
765, 769, 770, 772, 773, 780, 781, 782, 786, 788, 790, 796, 797, 802,
803, 804, 805, 812, 813, 817, 818, 820, 822, 828, 830, 834, 836, 837,
840, 841, 842, 843, 844, 846, 849, 850, 852, 854, 860, 862, 866, 867,
868, 869, 876, 877, 880, 882, 884, 886, 892, 894, 898, 900, 901, 908,
910, 913, 914, 916, 918, 924, 925, 930, 932, 933, 940, 941, 943, 944,
945, 946, 947, 948, 950, 956, 957, 961, 962, 964, 965, 972, 974, 978,
980, 982, 988, 990, 994, 996, 997, 998, 1004, 1005, 1008, 1010, 1012,
1014, 1020, 1022, 1025, 1026, 1028, 1029, 1034, 1035, 1036, 1038, 1041,
1042, 1044, 1046, 1052, 1053, 1058, 1060, 1061, 1068, 1069, 1073, 1074,
1076, 1078, 1084, 1086, 1089, 1090, 1092, 1093, 1100, 1102, 1106, 1108,
1110, 1116, 1118, 1121, 1122, 1123, 1124, 1125, 1132, 1133, 1134, 1138,
1140, 1142, 1148, 1149, 1154, 1155, 1156, 1157, 1164, 1166, 1169, 1170,
1172, 1173, 1174, 1175, 1179, 1180, 1181, 1186, 1187, 1188, 1189, 1195,
1196, 1197, 1201, 1202, 1204, 1206, 1212, 1213, 1217, 1218, 1220, 1221,
1228, 1230, 1233, 1234, 1236, 1238, 1244, 1246, 1250, 1252, 1253, 1256,
1257, 1260, 1261, 1264, 1266, 1268, 1270, 1276, 1278, 1281, 1282, 1284,
1285, 1292, 1294, 1298, 1300, 1302, 1308, 1309, 1314, 1315, 1316, 1317,
1324, 1325, 1329, 1330, 1332, 1334, 1340, 1342, 1346, 1348, 1349, 1356,
1358, 1362, 1364, 1366, 1372, 1374, 1378, 1379, 1380, 1381, 1388, 1389,
1392, 1394, 1396, 1398, 1404, 1406, 1410, 1412, 1413, 1415, 1420, 1422,
1425, 1426, 1428, 1430, 1436, 1437, 1442, 1443, 1444, 1445, 1452, 1453,
1457, 1458, 1460, 1462, 1468, 1469, 1474, 1476, 1477, 1484, 1486, 1490,
1492, 1494, 1495, 1496, 1497, 1498, 1499, 1500, 1502, 1506, 1508, 1509,
1516, 1517, 1520, 1522, 1524, 1526, 1532, 1534, 1538, 1539, 1540, 1541,
1548, 1550, 1552, 1554, 1556, 1558, 1564, 1565, 1570, 1572, 1573, 1574,
1580, 1581, 1585, 1586, 1588, 1590, 1592, 1593, 1596, 1598, 1601, 1602,
1604, 1605, 1610, 1611, 1612, 1614, 1617, 1618, 1620, 1622, 1628, 1630,
1634, 1635, 1636, 1637, 1644, 1645, 1646, 1650, 1652, 1654, 1660, 1661,
1666, 1668, 1669, 1671, 1676, 1678, 1680, 1681, 1682, 1683, 1684, 1685,
1686, 1687, 1692, 1693, 1698, 1699, 1700, 1701, 1702, 1708, 1709, 1713,
1714, 1716, 1718, 1724, 1725, 1730, 1732, 1733, 1740, 1742, 1745, 1746,
1748, 1750, 1752, 1753, 1756, 1758, 1762, 1764, 1765, 1771, 1772, 1773,
1778, 1780, 1782, 1788, 1789, 1790, 1794, 1796, 1797, 1804, 1806, 1810,
1812, 1814, 1820, 1821, 1826, 1827, 1828, 1829, 1835, 1836, 1837, 1841,
1842, 1844, 1846, 1850, 1851, 1852, 1854, 1858, 1860, 1861, 1868, 1870,
1874, 1876, 1878, 1884, 1886, 1887, 1890, 1891, 1892, 1893, 1900, 1901,
1904, 1906, 1908, 1910, 1916, 1918, 1922, 1923, 1924, 1925, 1926, 1932,
1934, 1937, 1938, 1940, 1942, 1948, 1949, 1954, 1956, 1957, 1964, 1965,
1969, 1970, 1972, 1974, 1980, 1981, 1986, 1988, 1989, 1991, 1992, 1993,
1994, 1995, 1996, 1997, 1998, 2002, 2004, 2006, 2012, 2014, 2018, 2020,
2021, 2028, 2029, 2034, 2036, 2038, 2044, 2045, 2050, 2051, 2052, 2053,
2054, 2060, 2062, 2064, 2066, 2068, 2069, 2070, 2071, 2076, 2077, 2082,
2083, 2084, 2085, 2092, 2093, 2097, 2098, 2100, 2102, 2108, 2110, 2113,
2114, 2116, 2117, 2124, 2126, 2130, 2132, 2134, 2140, 2142, 2146, 2147,
2148, 2149, 2156, 2157, 2162, 2164, 2166, 2172, 2173, 2178, 2179, 2180,
2181, 2188, 2190, 2193, 2194, 2196, 2198, 2204, 2205, 2210, 2212, 2213,
2220, 2221, 2225, 2226, 2228, 2230, 2234, 2236, 2237, 2241, 2242, 2243,
2244, 2245, 2248, 2249, 2252, 2254, 2257, 2258, 2260, 2262, 2264, 2265,
2268, 2269, 2270, 2274, 2276, 2277, 2284, 2285, 2288, 2290, 2292, 2294,
2300, 2302, 2306, 2308, 2309, 2316, 2318, 2322, 2324, 2326, 2332, 2333,
2337, 2338, 2339, 2340, 2341, 2348, 2349, 2353, 2354, 2356, 2358, 2359,
2360, 2361, 2362, 2363, 2364, 2366, 2370, 2372, 2373, 2378, 2379, 2380,
2382, 2385, 2386, 2388, 2390, 2391, 2396, 2398, 2402, 2403, 2404, 2405,
2412, 2413, 2416, 2418, 2420, 2422, 2428, 2430, 2434, 2435, 2436, 2437,
2438, 2444, 2446, 2449, 2450, 2452, 2454, 2460, 2461, 2466, 2467, 2468,
2469, 2470, 2476, 2477, 2481, 2482, 2484, 2486, 2492, 2493, 2498, 2500,
2501, 2508, 2510, 2514, 2515, 2516, 2518, 2520, 2521, 2524, 2526, 2530,
2532, 2533, 2540, 2541, 2546, 2548, 2550, 2554, 2556, 2557, 2562, 2563,
2564, 2565, 2572, 2574, 2578, 2580, 2582, 2588, 2589, 2594, 2596, 2597,
2598, 2603, 2604, 2605, 2609, 2610, 2612, 2614, 2620, 2622, 2625, 2626,
2628, 2629, 2634, 2635, 2636, 2638, 2641, 2642, 2644, 2646, 2652, 2654,
2657, 2658, 2659, 2660, 2661, 2668, 2669, 2674, 2676, 2678, 2682, 2684,
2685, 2686, 2690, 2692, 2693, 2700, 2702, 2705, 2706, 2708, 2710, 2716,
2717, 2718, 2722, 2724, 2725, 2732, 2733, 2737, 2738, 2740, 2742, 2748,
2749, 2754, 2756, 2757, 2760, 2761, 2764, 2766, 2769, 2770, 2772, 2774,
2776, 2777, 2780, 2782, 2786, 2788, 2789, 2795, 2796, 2797, 2798, 2802,
2804, 2806, 2812, 2813, 2817, 2818, 2820, 2821, 2828, 2830, 2831, 2834,
2836, 2838, 2844, 2845, 2850, 2851, 2852, 2853, 2860, 2861, 2865, 2866,
2868, 2870, 2874, 2875, 2876, 2878, 2882, 2884, 2885, 2890, 2891, 2892,
2894, 2897, 2898, 2900, 2902, 2904, 2905, 2908, 2910, 2914, 2915, 2916,
2917, 2923, 2924, 2925, 2928, 2930, 2932, 2934, 2940, 2942, 2946, 2948,
2949, 2956, 2958, 2961, 2962, 2964, 2966, 2970, 2972, 2973, 2978, 2980,
2981, 2987, 2988, 2989, 2990, 2991, 2992, 2993, 2994, 2995, 2996, 2997,
2998, 2999, 3004, 3005, 3009, 3010, 3012, 3013, 3018, 3019, 3020, 3022,
3025, 3026, 3028, 3030, 3036, 3038, 3042, 3044, 3045, 3051, 3052, 3053,
3058, 3060, 3062, 3067, 3068, 3069, 3074, 3076, 3077, 3082, 3083, 3084,
3086, 3090, 3092, 3094, 3100, 3101, 3106, 3108, 3109, 3110, 3115, 3116,
3117, 3121, 3122, 3124, 3126, 3132, 3134, 3137, 3138, 3140, 3141, 3144,
3145, 3148, 3149, 3150, 3154, 3156, 3158, 3164, 3166, 3170, 3171, 3172,
3173, 3180, 3181, 3186, 3187, 3188, 3190, 3195, 3196, 3197, 3202, 3203,
3204, 3205, 3212, 3214, 3217, 3218, 3220, 3221, 3222, 3223, 3228, 3229,
3234, 3235, 3236, 3237, 3244, 3245, 3249, 3250, 3252, 3254, 3260, 3261,
3265, 3266, 3268, 3269, 3276, 3278, 3281, 3282, 3284, 3286, 3288, 3289,
3290, 3291, 3292, 3293, 3294, 3298, 3300, 3301, 3308, 3309, 3312, 3314,
3316, 3318, 3324, 3326, 3330, 3332, 3333, 3340, 3342, 3343, 3346, 3348,
3350, 3352, 3353, 3356, 3357, 3360, 3361, 3362, 3363, 3364, 3365, 3372,
3373, 3377, 3378, 3380, 3382, 3388, 3390, 3394, 3396, 3397, 3402, 3403,
3404, 3405, 3406, 3409, 3410, 3412, 3414, 3416, 3417, 3420, 3422, 3426,
3427, 3428, 3429, 3435, 3436, 3437, 3438, 3440, 3442, 3444, 3446, 3452,
3454, 3458, 3460, 3461, 3468, 3470, 3473, 3474, 3476, 3478, 3484, 3485,
3490, 3491, 3492, 3493, 3500, 3501, 3504, 3505, 3506, 3507, 3508, 3510,
3512, 3513, 3515, 3516, 3517, 3521, 3522, 3524, 3525, 3532, 3534, 3538,
3540, 3542, 3543, 3544, 3545, 3546, 3547, 3548, 3550, 3554, 3556, 3557,
3564, 3565, 3568, 3570, 3572, 3574, 3580, 3581, 3582, 3586, 3588, 3589,
3596, 3598, 3602, 3604, 3606, 3612, 3613, 3618, 3620, 3621, 3627, 3628,
3629, 3633, 3634, 3636, 3638, 3644, 3646, 3649, 3650, 3652, 3653, 3658,
3659, 3660, 3662, 3665, 3666, 3668, 3670, 3671, 3676, 3678, 3681, 3682,
3683, 3684, 3685, 3691, 3692, 3693, 3698, 3700, 3701, 3702, 3703, 3706,
3708, 3709, 3714, 3716, 3717, 3724, 3726, 3729, 3730, 3732, 3734, 3740,
3741, 3746, 3748, 3749, 3756, 3757, 3758, 3761, 3762, 3764, 3766, 3772,
3773, 3778, 3780, 3781, 3788, 3790, 3793, 3794, 3796, 3798, 3800, 3801,
3804, 3806, 3810, 3812, 3813, 3819, 3820, 3821, 3826, 3828, 3830, 3832,
3833, 3835, 3836, 3837, 3842, 3844, 3845, 3852, 3853, 3854, 3858, 3860,
3862, 3868, 3869, 3873, 3874, 3875, 3876, 3877, 3884, 3885, 3889, 3890,
3892, 3894, 3896, 3897, 3898, 3899, 3900, 3902, 3906, 3908, 3909, 3916,
3918, 3922, 3924, 3926, 3932, 3934, 3938, 3939, 3940, 3941, 3948, 3949,
3952, 3954, 3956, 3958, 3964, 3966, 3970, 3972, 3973, 3980, 3982, 3983,
3984, 3985, 3986, 3987, 3988, 3989, 3990, 3991, 3992, 3993, 3996, 3997,
4002, 4004, 4005, 4012, 4013, 4014, 4017, 4018, 4020, 4022, 4024, 4025,
4026, 4028, 4029, 4030, 4033, 4034, 4036, 4037, 4044, 4046, 4050, 4052,
4054, 4060, 4062, 4066, 4068, 4069, 4070, 4076, 4077, 4078, 4080, 4082,
4084, 4086, 4088, 4089, 4092, 4094, 4098, 4100, 4101, 4106, 4107, 4108,
4109, 4110, 4114, 4116, 4118, 4124, 4125, 4130, 4132, 4133, 4140, 4141,
4145, 4146, 4148, 4150, 4152, 4153, 4154, 4155, 4156, 4158, 4161, 4162,
4164, 4165, 4170, 4171, 4172, 4174, 4178, 4180, 4182, 4188, 4190, 4193,
4194, 4195, 4196, 4197, 4198, 4204, 4205, 4210, 4212, 4214, 4220, 4221,
4226, 4227, 4228, 4229, 4236, 4238, 4241, 4242, 4244, 4246, 4248, 4249,
4252, 4253, 4258, 4260, 4261, 4268, 4269, 4273, 4274, 4276, 4278, 4284,
4285, 4289, 4290, 4292, 4293, 4296, 4297, 4300, 4302, 4305, 4306, 4308,
4310, 4312, 4313, 4316, 4318, 4322, 4324, 4325, 4332, 4333, 4336, 4338,
4340, 4342, 4348, 4350, 4353, 4354, 4356, 4357, 4364, 4366, 4370, 4372,
4374, 4380, 4381, 4382, 4385, 4386, 4387, 4388, 4389, 4396, 4397, 4401,
4402, 4404, 4406, 4410, 4411, 4412, 4414, 4418, 4420, 4421, 4428, 4430,
4434, 4436, 4438, 4444, 4446, 4450, 4451, 4452, 4453, 4456, 4457, 4458,
4460, 4461, 4463, 4464, 4466, 4468, 4469, 4470, 4476, 4478, 4481, 4482,
4483, 4484, 4485, 4486, 4487, 4492, 4494, 4496, 4497, 4498, 4499, 4500,
4502, 4508, 4509, 4514, 4515, 4516, 4517, 4524, 4525, 4526, 4528, 4529,
4530, 4531, 4532, 4534, 4536, 4537, 4540, 4541, 4545, 4546, 4548, 4549,
4554, 4555, 4556, 4558, 4562, 4564, 4566, 4568, 4569, 4572, 4574, 4578,
4580, 4581, 4588, 4589, 4594, 4596, 4598, 4604, 4605, 4610, 4612, 4613,
4620, 4622, 4624, 4626, 4628, 4630, 4636, 4637, 4642, 4644, 4645, 4652,
4653, 4657, 4658, 4660, 4662, 4666, 4667, 4668, 4670, 4673, 4674, 4675,
4676, 4677, 4682, 4683, 4684, 4686, 4689, 4690, 4692, 4694, 4700, 4702,
4706, 4707, 4708, 4709, 4716, 4717, 4722, 4723, 4724, 4725, 4726, 4727,
4728, 4729, 4730, 4732, 4733, 4738, 4740, 4741, 4748, 4750, 4753, 4754,
4756, 4757, 4758, 4759, 4764, 4765, 4770, 4771, 4772, 4773, 4780, 4781,
4785, 4786, 4788, 4790, 4796, 4797, 4802, 4804, 4805, 4812, 4814, 4817,
4818, 4820, 4822, 4828, 4830, 4834, 4836, 4837, 4844, 4845, 4850, 4852,
4854, 4860, 4861, 4865, 4866, 4868, 4869, 4876, 4877, 4878, 4882, 4884,
4886, 4892, 4893, 4898, 4899, 4900, 4901, 4907, 4908, 4909, 4913, 4914,
4916, 4918, 4920, 4921, 4922, 4923, 4924, 4926, 4930, 4932, 4933, 4936,
4937, 4938, 4939, 4940, 4941, 4942, 4945, 4946, 4948, 4950, 4956, 4958,
4962, 4963, 4964, 4965, 4971, 4972, 4973, 4974, 4976, 4978, 4980, 4982,
4988, 4990, 4994, 4996, 4997, 5004, 5006, 5009, 5010, 5012, 5014, 5020,
5021, 5022, 5026, 5028, 5029, 5036, 5037, 5040, 5041, 5042, 5043, 5044,
5046, 5052, 5053, 5057, 5058, 5060, 5061, 5066, 5067, 5068, 5070, 5074,
5076, 5078, 5084, 5086, 5090, 5092, 5093, 5100, 5101, 5102, 5104, 5106,
5108, 5109, 5110, 5112, 5113, 5116, 5118, 5122, 5124, 5125, 5130, 5131,
5132, 5134, 5137, 5138, 5140, 5142, 5148, 5149, 5154, 5156, 5157, 5158,
5163, 5164, 5165, 5169, 5170, 5172, 5174, 5180, 5182, 5185, 5186, 5188,
5189, 5196, 5197, 5198, 5202, 5204, 5206, 5207, 5212, 5214, 5218, 5219,
5220, 5221, 5228, 5229, 5234, 5236, 5238, 5244, 5245, 5250, 5251, 5252,
5253, 5260, 5262, 5265, 5266, 5268, 5269, 5270, 5271, 5276, 5277, 5282,
5283, 5284, 5285, 5291, 5292, 5293, 5297, 5298, 5300, 5302, 5308, 5309,
5313, 5314, 5315, 5316, 5317, 5318, 5319, 5320, 5321, 5322, 5323, 5324,
5326, 5329, 5330, 5332, 5334, 5340, 5342, 5346, 5348, 5349, 5356, 5357,
5360, 5362, 5364, 5365, 5366, 5372, 5373, 5374, 5377, 5378, 5380, 5381,
5388, 5390, 5394, 5396, 5398, 5404, 5405, 5410, 5411, 5412, 5413, 5414,
5420, 5421, 5425, 5426, 5428, 5430, 5436, 5437, 5438, 5442, 5444, 5445,
5452, 5454, 5458, 5460, 5462, 5468, 5470, 5474, 5475, 5476, 5477, 5483,
5484, 5485, 5488, 5490, 5492, 5494, 5500, 5502, 5506, 5508, 5509, 5511,
5516, 5518, 5520, 5521, 5522, 5523, 5524, 5526, 5532, 5533, 5537, 5538,
5539, 5540, 5541, 5548, 5549, 5550, 5552, 5553, 5554, 5555, 5556, 5558,
5560, 5561, 5563, 5564, 5565, 5570, 5572, 5573, 5580, 5582, 5586, 5588,
5590, 5591, 5592, 5593, 5596, 5597, 5598, 5602, 5604, 5605, 5612, 5613,
5616, 5618, 5620, 5622, 5628, 5630, 5634, 5635, 5636, 5637, 5638, 5644,
5646, 5650, 5652, 5654, 5660, 5661, 5665, 5666, 5668, 5669, 5670, 5675,
5676, 5677, 5681, 5682, 5684, 5686, 5692, 5694, 5697, 5698, 5700, 5701,
5706, 5707, 5708, 5710, 5713, 5714, 5716, 5718, 5724, 5726, 5729, 5730,
5731, 5732, 5733, 5740, 5741, 5742, 5746, 5748, 5749, 5750, 5751, 5754,
5756, 5757, 5762, 5764, 5765, 5772, 5774, 5777, 5778, 5780, 5781, 5782,
5783, 5788, 5789, 5794, 5795, 5796, 5797, 5804, 5805, 5808, 5809, 5810,
5811, 5812, 5814, 5819, 5820, 5821, 5822, 5826, 5828, 5829, 5836, 5838,
5841, 5842, 5844, 5846, 5847, 5848, 5849, 5850, 5851, 5852, 5854, 5858,
5860, 5861, 5868, 5869, 5874, 5876, 5878, 5880, 5881, 5884, 5885, 5890,
5892, 5893, 5900, 5902, 5906, 5908, 5910, 5916, 5917, 5922, 5923, 5924,
5925, 5932, 5933, 5937, 5938, 5940, 5941, 5942, 5948, 5950, 5954, 5956,
5957, 5964, 5966, 5970, 5972, 5974, 5975, 5976, 5977, 5980, 5981, 5982,
5983, 5986, 5987, 5988, 5989, 5996, 5997, 6000, 6002, 6004, 6006, 6012,
6014, 6018, 6019, 6020, 6021, 6022, 6028, 6030, 6033, 6034, 6036, 6037,
6038, 6039, 6040, 6041, 6044, 6045, 6046, 6049, 6050, 6051, 6052, 6053,
6059, 6060, 6061, 6062, 6065, 6066, 6068, 6070, 6072, 6073, 6074, 6076,
6077, 6082, 6084, 6085, 6090, 6091, 6092, 6094, 6098, 6100, 6102, 6103,
6106, 6107, 6108, 6110, 6114, 6116, 6117, 6118, 6124, 6125, 6126, 6128,
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7058, 7060, 7062, 7068, 7069, 7074, 7076, 7077, 7083, 7084, 7085, 7086, 7087, 7088, 7089, 7090, 7091, 7092, 7093, 7094, 7095, 7096, 7097, 7098, 7100, 7101, 7105, 7106, 7108, 7109, 7111, 7116, 7118, 7122, 7124, 7126, 7132, 7134, 7138, 7140, 7141, 7148, 7149, 7151, 7153, 7154, 7156, 7158, 7164, 7165, 7169, 7170, 7172, 7173, 7180, 7182, 7186, 7188, 7190, 7194, 7196, 7197, 7202, 7204, 7205, 7212, 7213, 7217, 7218, 7220, 7222, 7228, 7230, 7233, 7234, 7236, 7237, 7244, 7246, 7249, 7250, 7252, 7254, 7255, 7260, 7262, 7266, 7267, 7268, 7269, 7276, 7277, 7282, 7284, 7286, 7291, 7292, 7293, 7298, 7299, 7300, 7301, 7308, 7310, 7313, 7314, 7316, 7317, 7318, 7319, 7324, 7325, 7330, 7331, 7332, 7333, 7340, 7341, 7345, 7346, 7348, 7350, 7356, 7357, 7361, 7362, 7363, 7364, 7365, 7372, 7374, 7377, 7378, 7380, 7382, 7383, 7384, 7385, 7386, 7387, 7388, 7390, 7394, 7396, 7397, 7404, 7405, 7408, 7410, 7412, 7413, 7414, 7416, 7417, 7420, 7422, 7426, 7428, 7429, 7436, 7438, 7442, 7444, 7446, 7452, 7453, 7454, 7457, 7458, 7459, 7460, 7461, 7462, 7468, 7469, 7473, 7474, 7476, 7478, 7484, 7486, 7490, 7492, 7493, 7500, 7502, 7506, 7508, 7510, 7512, 7513, 7516, 7517, 7518, 7522, 7523, 7524, 7525, 7532, 7533, 7534, 7536, 7538, 7540, 7542, 7548, 7550, 7553, 7554, 7556, 7557, 7564, 7566, 7569, 7570, 7572, 7574, 7580, 7581, 7586, 7587, 7588, 7589, 7596, 7597, 7600, 7601, 7602, 7603, 7604, 7606, 7608, 7609, 7611, 7612, 7613, 7617, 7618, 7620, 7621, 7628, 7630, 7634, 7636, 7638, 7639, 7640, 7641, 7644, 7646, 7650, 7652, 7653, 7654, 7659, 7660, 7661, 7664, 7665, 7666, 7667, 7668, 7670, 7671, 7676, 7678, 7682, 7684, 7685, 7692, 7694, 7696, 7698, 7700, 7702, 7708, 7709, 7714, 7716, 7717, 7724, 7725, 7729, 7730, 7732, 7734, 7738, 7739, 7740, 7742, 7745, 7746, 7747, 7748, 7749, 7754, 7755, 7756, 7758, 7761, 7762, 7764, 7766, 7772, 7774, 7778, 7779, 7780, 7781, 7788, 7789, 7794, 7795, 7796, 7797, 7798, 7799, 7800, 7801, 7802, 7804, 7805, 7810, 7812, 7813, 7820, 7822, 7825, 7826, 7828, 7830, 7836, 7837, 7838, 7841, 7842, 7844, 7845, 7851, 7852, 7853, 7854, 7857, 7858, 7860, 7862, 7868, 7869, 7874, 7876, 7877, 7884, 7886, 7889, 7890, 7892, 7894, 7896, 7897, 7900, 7902, 7906, 7908, 7909, 7916, 7917, 7921, 7922, 7924, 7926, 7932, 7933, 7938, 7940, 7941, 7948, 7950, 7954, 7956, 7958, 7964, 7965, 7968, 7969, 7970, 7971, 7972, 7973, 7976, 7977, 7978, 7979, 7980, 7981, 7982, 7983, 7984, 7985, 7986, 7987, 7988, 7990, 7994, 7995, 7996, 7998, 8002, 8004, 8005, 8012, 8014, 8018, 8020, 8022, 8024, 8025, 8028, 8029, 8030, 8034, 8035, 8036, 8037, 8044, 8045, 8046, 8048, 8049, 8050, 8051, 8052, 8053, 8054, 8060, 8061, 8062, 8065, 8066, 8067, 8068, 8069, 8070, 8076, 8078, 8081, 8082, 8084, 8086, 8092, 8093, 8095, 8097, 8098, 8100, 8101, 8108, 8109, 8113, 8114, 8116, 8118, 8120, 8121, 8122, 8124, 8125, 8130, 8132, 8133, 8136, 8137, 8140, 8141, 8142, 8146, 8148, 8150, 8156, 8157, 8158, 8162, 8164, 8165, 8172, 8173, 8178, 8179, 8180, 8182, 8188, 8189, 8190, 8194, 8196, 8197, 8204, 8206, 8208, 8210, 8212, 8213, 8214, 8215, 8220, 8221, 8226, 8228, 8229, 8236, 8237, 8241, 8242, 8244, 8246, 8252, 8254, 8257, 8258, 8260, 8261, 8263, 8268, 8270, 8274, 8276, 8278, 8284, 8286, 8290, 8291, 8292, 8293, 8300, 8301, 8306, 8307, 8308, 8309, 8310, 8311, 8316, 8317, 8322, 8323, 8324, 8325, 8326, 8332, 8334, 8337, 8338, 8340, 8341, 8342, 8343, 8348, 8349, 8354, 8356, 8357, 8364, 8365, 8369, 8370, 8372, 8374, 8380, 8381, 8385, 8386, 8387, 8388, 8389, 8390, 8391, 8394, 8395, 8396, 8397, 8398, 8401, 8402, 8404, 8406, 8412, 8414, 8418, 8420, 8421, 8427, 8428, 8429, 8432, 8434, 8436, 8438, 8444, 8446, 8449, 8450, 8452, 8453, 8458, 8459, 8460, 8462, 8466, 8468, 8470, 8476, 8477, 8478, 8481, 8482, 8483, 8484, 8485, 8492, 8493, 8496, 8497, 8498, 8499, 8500, 8502, 8506, 8507, 8508, 8510, 8514, 8516, 8517, 8520, 8521, 8524, 8526, 8530, 8532, 8534, 8540, 8542, 8546, 8547, 8548, 8549, 8556, 8557, 8558, 8560, 8562, 8564, 8566, 8570, 8571, 8572, 8574, 8578, 8579, 8580, 8581, 8582, 8588, 8590, 8592, 8593, 8594, 8595, 8596, 8598, 8604, 8605, 8610, 8611, 8612, 8613, 8614, 8620, 8621, 8624, 8625, 8626, 8627, 8628, 8630, 8632, 8633, 8636, 8637, 8641, 8642, 8644, 8645, 8652, 8654, 8658, 8660, 8662, 8664, 8665, 8668, 8670, 8674, 8676, 8677, 8684, 8685, 8690, 8692, 8694, 8700, 8701, 8706, 8707, 8708, 8709, 8716, 8718, 8720, 8722, 8724, 8726, 8732, 8733, 8734, 8738, 8740, 8741, 8742, 8748, 8749, 8753, 8754, 8756, 8758, 8764, 8765, 8766, 8769, 8770, 8771, 8772, 8773, 8774, 8775, 8776, 8777, 8778, 8779, 8780, 8782, 8785, 8786, 8788, 8790, 8796, 8798, 8802, 8803, 8804, 8805, 8811, 8812, 8813, 8814, 8818, 8820, 8821, 8822, 8823, 8828, 8829, 8834, 8836, 8837, 8838, 8844, 8846, 8849, 8850, 8852, 8854, 8860, 8861, 8866, 8868, 8869, 8870, 8875, 8876, 8877, 8881, 8882, 8884, 8886, 8892, 8893, 8898, 8900, 8901, 8908, 8910, 8912, 8913, 8914, 8915, 8916, 8917, 8918, 8924, 8926, 8927, 8930, 8932, 8933, 8940, 8941, 8946, 8948, 8950, 8956, 8957, 8961, 8962, 8963, 8964, 8965, 8972, 8973, 8974, 8975, 8976, 8978, 8980, 8982, 8988, 8989, 8994, 8995, 8996, 8997, 9004, 9005, 9009, 9010, 9012, 9014, 9020, 9022, 9026, 9028, 9029, 9034, 9035, 9036, 9038, 9041, 9042, 9044, 9046, 9052, 9053, 9054, 9058, 9059, 9060, 9061, 9068, 9069, 9070, 9072, 9073, 9074, 9075, 9076, 9078, 9084, 9086, 9089, 9090, 9091, 9092, 9093, 9094, 9100, 9102, 9105, 9106, 9108, 9109, 9110, 9111, 9112, 9113, 9115, 9116, 9117, 9121, 9122, 9124, 9125, 9126, 9132, 9133, 9134, 9136, 9137, 9138, 9139, 9140, 9142, 9148, 9149, 9153, 9154, 9156, 9157, 9160, 9161, 9164, 9166, 9169, 9170, 9172, 9174, 9178, 9179, 9180, 9182, 9186, 9188, 9189, 9190, 9195, 9196, 9197, 9200, 9202, 9204, 9206, 9212, 9214, 9217, 9218, 9220, 9221, 9228, 9230, 9234, 9236, 9238, 9244, 9245, 9250, 9252, 9253, 9260, 9261, 9265, 9266, 9268, 9270, 9276, 9278, 9281, 9282, 9284, 9285, 9292, 9294, 9298, 9300, 9302, 9308, 9310, 9314, 9315, 9316, 9317, 9324, 9325, 9330, 9332, 9333, 9334, 9335, 9340, 9341, 9346, 9347, 9348, 9349, 9356, 9358, 9361, 9362, 9364, 9365, 9366, 9367, 9368, 9369, 9372, 9373, 9378, 9379, 9380, 9381, 9388, 9389, 9393, 9394, 9396, 9398, 9403, 9404, 9405, 9409, 9410, 9412, 9413, 9420, 9422, 9425, 9426, 9428, 9430, 9436, 9438, 9442, 9444, 9445, 9448, 9449, 9452, 9453, 9456, 9457, 9458, 9459, 9460, 9461, 9462, 9468, 9470, 9473, 9474, 9476, 9477, 9480, 9481, 9484, 9486, 9490, 9492, 9494, 9500, 9501, 9506, 9507, 9508, 9509, 9510, 9516, 9517, 9521, 9522, 9524, 9526, 9532, 9534, 9537, 9538, 9540, 9541, 9546, 9547, 9548, 9550, 9553, 9554, 9556, 9558, 9564, 9566, 9570, 9571, 9572, 9573, 9580, 9581, 9584, 9586, 9588, 9590, 9594, 9595, 9596, 9598, 9602, 9604, 9605, 9612, 9614, 9617, 9618, 9620, 9622, 9628, 9629, 9634, 9635, 9636, 9637, 9643, 9644, 9645, 9649, 9650, 9652, 9654, 9660, 9661, 9665, 9666, 9668, 9669, 9672, 9673, 9676, 9678, 9682, 9684, 9686, 9688, 9689, 9692, 9694, 9698, 9700, 9701, 9708, 9709, 9712, 9714, 9716, 9718, 9720, 9721, 9724, 9726, 9730, 9731, 9732, 9733, 9734, 9740, 9742, 9744, 9746, 9748, 9750, 9756, 9757, 9762, 9764, 9765, 9766, 9772, 9773, 9777, 9778, 9780, 9782, 9788, 9790, 9793, 9794, 9796, 9797, 9802, 9803, 9804, 9806, 9809, 9810, 9812, 9814, 9815, 9816, 9817, 9820, 9822, 9826, 9827, 9828, 9829, 9836, 9837, 9842, 9843, 9844, 9845, 9846, 9847, 9848, 9849, 9850, 9852, 9853, 9858, 9860, 9861, 9862, 9868, 9870, 9872, 9873, 9874, 9875, 9876, 9877, 9878, 9879, 9884, 9885, 9889, 9890, 9891, 9892, 9893, 9894, 9900, 9901, 9902, 9905, 9906, 9908, 9910, 9915, 9916, 9917, 9922, 9924, 9925, 9932, 9934, 9937, 9938, 9940, 9942, 9943, 9944, 9945, 9948, 9949, 9950, 9954, 9956, 9957, 9964, 9965, 9970, 9972, 9974, 9979, 9980, 9981, 9986, 9988, 9989, 9996, 9998]
len(paired_values) 
       
4161
4161
N=10000 triple_values=[] for i in srange(N): if h(i)==h(i+1) and h(i)==h(i+2): triple_values.append(i) print(triple_values) len(triple_values) 
       
[28, 36, 44, 49, 65, 68, 98, 99, 100, 108, 124, 130, 131, 132, 145, 156,
164, 172, 177, 188, 193, 196, 209, 228, 236, 257, 260, 284, 290, 291,
292, 300, 305, 314, 315, 324, 354, 355, 356, 364, 386, 387, 388, 389,
401, 412, 418, 419, 420, 428, 433, 444, 452, 472, 484, 492, 508, 514,
515, 516, 540, 548, 556, 561, 577, 580, 586, 587, 593, 610, 611, 612,
620, 628, 629, 630, 636, 644, 657, 668, 676, 684, 689, 700, 708, 721,
740, 747, 748, 764, 769, 772, 780, 781, 796, 802, 803, 804, 812, 817,
836, 840, 841, 842, 843, 849, 866, 867, 868, 876, 900, 913, 924, 932,
940, 943, 944, 945, 946, 947, 956, 961, 964, 996, 997, 1004, 1025, 1028,
1034, 1035, 1041, 1052, 1060, 1068, 1073, 1089, 1092, 1121, 1122, 1123,
1124, 1132, 1133, 1148, 1154, 1155, 1156, 1169, 1172, 1173, 1174, 1179,
1180, 1186, 1187, 1188, 1195, 1196, 1201, 1212, 1217, 1220, 1233, 1252,
1256, 1260, 1281, 1284, 1308, 1314, 1315, 1316, 1324, 1329, 1348, 1378,
1379, 1380, 1388, 1412, 1425, 1436, 1442, 1443, 1444, 1452, 1457, 1468,
1476, 1494, 1495, 1496, 1497, 1498, 1499, 1508, 1516, 1538, 1539, 1540,
1564, 1572, 1573, 1580, 1585, 1592, 1601, 1604, 1610, 1611, 1617, 1634,
1635, 1636, 1644, 1645, 1660, 1668, 1680, 1681, 1682, 1683, 1684, 1685,
1686, 1692, 1698, 1699, 1700, 1701, 1708, 1713, 1724, 1732, 1745, 1752,
1764, 1771, 1772, 1788, 1789, 1796, 1820, 1826, 1827, 1828, 1835, 1836,
1841, 1850, 1851, 1860, 1886, 1890, 1891, 1892, 1900, 1922, 1923, 1924,
1925, 1937, 1948, 1956, 1964, 1969, 1980, 1988, 1991, 1992, 1993, 1994,
1995, 1996, 1997, 2020, 2028, 2044, 2050, 2051, 2052, 2053, 2068, 2069,
2070, 2076, 2082, 2083, 2084, 2092, 2097, 2113, 2116, 2146, 2147, 2148,
2156, 2172, 2178, 2179, 2180, 2193, 2204, 2212, 2220, 2225, 2236, 2241,
2242, 2243, 2244, 2248, 2257, 2264, 2268, 2269, 2276, 2284, 2308, 2332,
2337, 2338, 2339, 2340, 2348, 2353, 2358, 2359, 2360, 2361, 2362, 2363,
2372, 2378, 2379, 2385, 2390, 2402, 2403, 2404, 2412, 2434, 2435, 2436,
2437, 2449, 2460, 2466, 2467, 2468, 2469, 2476, 2481, 2492, 2500, 2514,
2515, 2520, 2532, 2540, 2556, 2562, 2563, 2564, 2588, 2596, 2597, 2603,
2604, 2609, 2625, 2628, 2634, 2635, 2641, 2657, 2658, 2659, 2660, 2668,
2684, 2685, 2692, 2705, 2716, 2717, 2724, 2732, 2737, 2748, 2756, 2760,
2769, 2776, 2788, 2795, 2796, 2797, 2812, 2817, 2820, 2830, 2844, 2850,
2851, 2852, 2860, 2865, 2874, 2875, 2884, 2890, 2891, 2897, 2904, 2914,
2915, 2916, 2923, 2924, 2948, 2961, 2972, 2980, 2987, 2988, 2989, 2990,
2991, 2992, 2993, 2994, 2995, 2996, 2997, 2998, 3004, 3009, 3012, 3018,
3019, 3025, 3044, 3051, 3052, 3067, 3068, 3076, 3082, 3083, 3100, 3108,
3109, 3115, 3116, 3121, 3137, 3140, 3144, 3148, 3149, 3170, 3171, 3172,
3180, 3186, 3187, 3195, 3196, 3202, 3203, 3204, 3217, 3220, 3221, 3222,
3228, 3234, 3235, 3236, 3244, 3249, 3260, 3265, 3268, 3281, 3288, 3289,
3290, 3291, 3292, 3293, 3300, 3308, 3332, 3342, 3352, 3356, 3360, 3361,
3362, 3363, 3364, 3372, 3377, 3396, 3402, 3403, 3404, 3405, 3409, 3416,
3426, 3427, 3428, 3435, 3436, 3437, 3460, 3473, 3484, 3490, 3491, 3492,
3500, 3504, 3505, 3506, 3507, 3512, 3515, 3516, 3521, 3524, 3542, 3543,
3544, 3545, 3546, 3547, 3556, 3564, 3580, 3581, 3588, 3612, 3620, 3627,
3628, 3633, 3649, 3652, 3658, 3659, 3665, 3670, 3681, 3682, 3683, 3684,
3691, 3692, 3700, 3701, 3702, 3708, 3716, 3729, 3740, 3748, 3756, 3757,
3761, 3772, 3780, 3793, 3800, 3812, 3819, 3820, 3832, 3835, 3836, 3844,
3852, 3853, 3868, 3873, 3874, 3875, 3876, 3884, 3889, 3896, 3897, 3898,
3899, 3908, 3938, 3939, 3940, 3948, 3972, 3982, 3983, 3984, 3985, 3986,
3987, 3988, 3989, 3990, 3991, 3992, 3996, 4004, 4012, 4013, 4017, 4024,
4025, 4028, 4029, 4033, 4036, 4068, 4069, 4076, 4077, 4088, 4100, 4106,
4107, 4108, 4109, 4124, 4132, 4140, 4145, 4152, 4153, 4154, 4155, 4161,
4164, 4170, 4171, 4193, 4194, 4195, 4196, 4197, 4204, 4220, 4226, 4227,
4228, 4241, 4248, 4252, 4260, 4268, 4273, 4284, 4289, 4292, 4296, 4305,
4312, 4324, 4332, 4353, 4356, 4380, 4381, 4385, 4386, 4387, 4388, 4396,
4401, 4410, 4411, 4420, 4450, 4451, 4452, 4456, 4457, 4460, 4463, 4468,
4469, 4481, 4482, 4483, 4484, 4485, 4486, 4496, 4497, 4498, 4499, 4508,
4514, 4515, 4516, 4524, 4525, 4528, 4529, 4530, 4531, 4536, 4540, 4545,
4548, 4554, 4555, 4568, 4580, 4588, 4604, 4612, 4636, 4644, 4652, 4657,
4666, 4667, 4673, 4674, 4675, 4676, 4682, 4683, 4689, 4706, 4707, 4708,
4716, 4722, 4723, 4724, 4725, 4726, 4727, 4728, 4729, 4732, 4740, 4753,
4756, 4757, 4758, 4764, 4770, 4771, 4772, 4780, 4785, 4796, 4804, 4817,
4836, 4844, 4860, 4865, 4868, 4876, 4877, 4892, 4898, 4899, 4900, 4907,
4908, 4913, 4920, 4921, 4922, 4923, 4932, 4936, 4937, 4938, 4939, 4940,
4941, 4945, 4962, 4963, 4964, 4971, 4972, 4973, 4996, 5009, 5020, 5021,
5028, 5036, 5040, 5041, 5042, 5043, 5052, 5057, 5060, 5066, 5067, 5092,
5100, 5101, 5108, 5109, 5112, 5124, 5130, 5131, 5137, 5148, 5156, 5157,
5163, 5164, 5169, 5185, 5188, 5196, 5197, 5206, 5218, 5219, 5220, 5228,
5244, 5250, 5251, 5252, 5265, 5268, 5269, 5270, 5276, 5282, 5283, 5284,
5291, 5292, 5297, 5308, 5313, 5314, 5315, 5316, 5317, 5318, 5319, 5320,
5321, 5322, 5323, 5329, 5348, 5356, 5364, 5365, 5372, 5373, 5377, 5380,
5404, 5410, 5411, 5412, 5413, 5420, 5425, 5436, 5437, 5444, 5474, 5475,
5476, 5483, 5484, 5508, 5520, 5521, 5522, 5523, 5532, 5537, 5538, 5539,
5540, 5548, 5549, 5552, 5553, 5554, 5555, 5560, 5563, 5564, 5572, 5590,
5591, 5592, 5596, 5597, 5604, 5612, 5634, 5635, 5636, 5637, 5660, 5665,
5668, 5669, 5675, 5676, 5681, 5697, 5700, 5706, 5707, 5713, 5729, 5730,
5731, 5732, 5740, 5741, 5748, 5749, 5750, 5756, 5764, 5777, 5780, 5781,
5782, 5788, 5794, 5795, 5796, 5804, 5808, 5809, 5810, 5811, 5819, 5820,
5821, 5828, 5841, 5846, 5847, 5848, 5849, 5850, 5851, 5860, 5868, 5880,
5884, 5892, 5916, 5922, 5923, 5924, 5932, 5937, 5940, 5941, 5956, 5974,
5975, 5976, 5980, 5981, 5982, 5986, 5987, 5988, 5996, 6018, 6019, 6020,
6021, 6033, 6036, 6037, 6038, 6039, 6040, 6044, 6045, 6049, 6050, 6051,
6052, 6059, 6060, 6061, 6065, 6072, 6073, 6076, 6084, 6090, 6091, 6102,
6106, 6107, 6116, 6117, 6124, 6125, 6134, 6148, 6164, 6165, 6166, 6172,
6180, 6188, 6193, 6209, 6212, 6220, 6221, 6230, 6231, 6232, 6242, 6243,
6244, 6252, 6267, 6268, 6274, 6275, 6276, 6288, 6289, 6290, 6291, 6296,
6297, 6298, 6299, 6300, 6305, 6308, 6316, 6321, 6332, 6337, 6340, 6344,
6353, 6360, 6372, 6380, 6390, 6404, 6428, 6434, 6435, 6436, 6444, 6449,
6458, 6459, 6468, 6474, 6475, 6481, 6498, 6499, 6500, 6508, 6509, 6530,
6531, 6532, 6533, 6545, 6556, 6561, 6562, 6563, 6564, 6565, 6572, 6573,
6576, 6577, 6578, 6579, 6580, 6581, 6582, 6583, 6584, 6588, 6593, 6596,
6616, 6628, 6636, 6652, 6660, 6684, 6692, 6699, 6700, 6704, 6705, 6706,
6707, 6720, 6721, 6722, 6723, 6724, 6730, 6731, 6737, 6754, 6755, 6756,
6764, 6780, 6781, 6788, 6789, 6801, 6804, 6805, 6806, 6812, 6817, 6818,
6819, 6820, 6828, 6832, 6833, 6834, 6835, 6840, 6844, 6849, 6852, 6865,
6870, 6876, 6877, 6884, 6892, 6908, 6913, 6916, 6929, 6940, 6946, 6947,
6948, 6956, 6961, 6980, 6986, 6987, 6993, 7000, 7010, 7011, 7012, 7019,
7020, 7024, 7025, 7026, 7027, 7030, 7042, 7043, 7044, 7045, 7057, 7068,
7076, 7083, 7084, 7085, 7086, 7087, 7088, 7089, 7090, 7091, 7092, 7093,
7094, 7095, 7096, 7097, 7100, 7105, 7108, 7140, 7148, 7153, 7164, 7169,
7172, 7196, 7204, 7212, 7217, 7233, 7236, 7249, 7254, 7266, 7267, 7268,
7276, 7291, 7292, 7298, 7299, 7300, 7313, 7316, 7317, 7318, 7324, 7330,
7331, 7332, 7340, 7345, 7356, 7361, 7362, 7363, 7364, 7377, 7382, 7383,
7384, 7385, 7386, 7387, 7396, 7404, 7412, 7413, 7416, 7428, 7452, 7453,
7457, 7458, 7459, 7460, 7461, 7468, 7473, 7492, 7512, 7516, 7517, 7522,
7523, 7524, 7532, 7533, 7553, 7556, 7569, 7580, 7586, 7587, 7588, 7596,
7600, 7601, 7602, 7603, 7608, 7611, 7612, 7617, 7620, 7638, 7639, 7640,
7652, 7653, 7659, 7660, 7664, 7665, 7666, 7667, 7670, 7684, 7708, 7716,
7724, 7729, 7738, 7739, 7745, 7746, 7747, 7748, 7754, 7755, 7761, 7778,
7779, 7780, 7788, 7794, 7795, 7796, 7797, 7798, 7799, 7800, 7801, 7804,
7812, 7825, 7836, 7837, 7841, 7844, 7851, 7852, 7853, 7857, 7868, 7876,
7889, 7896, 7908, 7916, 7921, 7932, 7940, 7964, 7968, 7969, 7970, 7971,
7972, 7976, 7977, 7978, 7979, 7980, 7981, 7982, 7983, 7984, 7985, 7986,
7987, 7994, 7995, 8004, 8024, 8028, 8029, 8034, 8035, 8036, 8044, 8045,
8048, 8049, 8050, 8051, 8052, 8053, 8060, 8061, 8065, 8066, 8067, 8068,
8069, 8081, 8092, 8097, 8100, 8108, 8113, 8120, 8121, 8124, 8132, 8136,
8140, 8141, 8156, 8157, 8164, 8172, 8178, 8179, 8188, 8189, 8196, 8212,
8213, 8214, 8220, 8228, 8236, 8241, 8257, 8260, 8290, 8291, 8292, 8300,
8306, 8307, 8308, 8309, 8310, 8316, 8322, 8323, 8324, 8325, 8337, 8340,
8341, 8342, 8348, 8356, 8364, 8369, 8380, 8385, 8386, 8387, 8388, 8389,
8390, 8394, 8395, 8396, 8397, 8401, 8420, 8427, 8428, 8449, 8452, 8458,
8459, 8476, 8477, 8481, 8482, 8483, 8484, 8492, 8496, 8497, 8498, 8499,
8506, 8507, 8516, 8520, 8546, 8547, 8548, 8556, 8557, 8570, 8571, 8578,
8579, 8580, 8581, 8592, 8593, 8594, 8595, 8604, 8610, 8611, 8612, 8613,
8620, 8624, 8625, 8626, 8627, 8632, 8636, 8641, 8644, 8664, 8676, 8684,
8700, 8706, 8707, 8708, 8732, 8733, 8740, 8741, 8748, 8753, 8764, 8765,
8769, 8770, 8771, 8772, 8773, 8774, 8775, 8776, 8777, 8778, 8779, 8785,
8802, 8803, 8804, 8811, 8812, 8813, 8820, 8821, 8822, 8828, 8836, 8837,
8849, 8860, 8868, 8869, 8875, 8876, 8881, 8892, 8900, 8912, 8913, 8914,
8915, 8916, 8917, 8926, 8932, 8940, 8956, 8961, 8962, 8963, 8964, 8972,
8973, 8974, 8975, 8988, 8994, 8995, 8996, 9004, 9009, 9028, 9034, 9035,
9041, 9052, 9053, 9058, 9059, 9060, 9068, 9069, 9072, 9073, 9074, 9075,
9089, 9090, 9091, 9092, 9093, 9105, 9108, 9109, 9110, 9111, 9112, 9115,
9116, 9121, 9124, 9125, 9132, 9133, 9136, 9137, 9138, 9139, 9148, 9153,
9156, 9160, 9169, 9178, 9179, 9188, 9189, 9195, 9196, 9217, 9220, 9244,
9252, 9260, 9265, 9281, 9284, 9314, 9315, 9316, 9324, 9332, 9333, 9334,
9340, 9346, 9347, 9348, 9361, 9364, 9365, 9366, 9367, 9368, 9372, 9378,
9379, 9380, 9388, 9393, 9403, 9404, 9409, 9412, 9425, 9444, 9448, 9452,
9456, 9457, 9458, 9459, 9460, 9461, 9473, 9476, 9480, 9500, 9506, 9507,
9508, 9509, 9516, 9521, 9537, 9540, 9546, 9547, 9553, 9570, 9571, 9572,
9580, 9594, 9595, 9604, 9617, 9628, 9634, 9635, 9636, 9643, 9644, 9649,
9660, 9665, 9668, 9672, 9688, 9700, 9708, 9720, 9730, 9731, 9732, 9733,
9756, 9764, 9765, 9772, 9777, 9793, 9796, 9802, 9803, 9809, 9814, 9815,
9816, 9826, 9827, 9828, 9836, 9842, 9843, 9844, 9845, 9846, 9847, 9848,
9849, 9852, 9860, 9861, 9872, 9873, 9874, 9875, 9876, 9877, 9878, 9884,
9889, 9890, 9891, 9892, 9893, 9900, 9901, 9905, 9915, 9916, 9924, 9937,
9942, 9943, 9944, 9948, 9949, 9956, 9964, 9979, 9980, 9988]
1782
[28, 36, 44, 49, 65, 68, 98, 99, 100, 108, 124, 130, 131, 132, 145, 156, 164, 172, 177, 188, 193, 196, 209, 228, 236, 257, 260, 284, 290, 291, 292, 300, 305, 314, 315, 324, 354, 355, 356, 364, 386, 387, 388, 389, 401, 412, 418, 419, 420, 428, 433, 444, 452, 472, 484, 492, 508, 514, 515, 516, 540, 548, 556, 561, 577, 580, 586, 587, 593, 610, 611, 612, 620, 628, 629, 630, 636, 644, 657, 668, 676, 684, 689, 700, 708, 721, 740, 747, 748, 764, 769, 772, 780, 781, 796, 802, 803, 804, 812, 817, 836, 840, 841, 842, 843, 849, 866, 867, 868, 876, 900, 913, 924, 932, 940, 943, 944, 945, 946, 947, 956, 961, 964, 996, 997, 1004, 1025, 1028, 1034, 1035, 1041, 1052, 1060, 1068, 1073, 1089, 1092, 1121, 1122, 1123, 1124, 1132, 1133, 1148, 1154, 1155, 1156, 1169, 1172, 1173, 1174, 1179, 1180, 1186, 1187, 1188, 1195, 1196, 1201, 1212, 1217, 1220, 1233, 1252, 1256, 1260, 1281, 1284, 1308, 1314, 1315, 1316, 1324, 1329, 1348, 1378, 1379, 1380, 1388, 1412, 1425, 1436, 1442, 1443, 1444, 1452, 1457, 1468, 1476, 1494, 1495, 1496, 1497, 1498, 1499, 1508, 1516, 1538, 1539, 1540, 1564, 1572, 1573, 1580, 1585, 1592, 1601, 1604, 1610, 1611, 1617, 1634, 1635, 1636, 1644, 1645, 1660, 1668, 1680, 1681, 1682, 1683, 1684, 1685, 1686, 1692, 1698, 1699, 1700, 1701, 1708, 1713, 1724, 1732, 1745, 1752, 1764, 1771, 1772, 1788, 1789, 1796, 1820, 1826, 1827, 1828, 1835, 1836, 1841, 1850, 1851, 1860, 1886, 1890, 1891, 1892, 1900, 1922, 1923, 1924, 1925, 1937, 1948, 1956, 1964, 1969, 1980, 1988, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 2020, 2028, 2044, 2050, 2051, 2052, 2053, 2068, 2069, 2070, 2076, 2082, 2083, 2084, 2092, 2097, 2113, 2116, 2146, 2147, 2148, 2156, 2172, 2178, 2179, 2180, 2193, 2204, 2212, 2220, 2225, 2236, 2241, 2242, 2243, 2244, 2248, 2257, 2264, 2268, 2269, 2276, 2284, 2308, 2332, 2337, 2338, 2339, 2340, 2348, 2353, 2358, 2359, 2360, 2361, 2362, 2363, 2372, 2378, 2379, 2385, 2390, 2402, 2403, 2404, 2412, 2434, 2435, 2436, 2437, 2449, 2460, 2466, 2467, 2468, 2469, 2476, 2481, 2492, 2500, 2514, 2515, 2520, 2532, 2540, 2556, 2562, 2563, 2564, 2588, 2596, 2597, 2603, 2604, 2609, 2625, 2628, 2634, 2635, 2641, 2657, 2658, 2659, 2660, 2668, 2684, 2685, 2692, 2705, 2716, 2717, 2724, 2732, 2737, 2748, 2756, 2760, 2769, 2776, 2788, 2795, 2796, 2797, 2812, 2817, 2820, 2830, 2844, 2850, 2851, 2852, 2860, 2865, 2874, 2875, 2884, 2890, 2891, 2897, 2904, 2914, 2915, 2916, 2923, 2924, 2948, 2961, 2972, 2980, 2987, 2988, 2989, 2990, 2991, 2992, 2993, 2994, 2995, 2996, 2997, 2998, 3004, 3009, 3012, 3018, 3019, 3025, 3044, 3051, 3052, 3067, 3068, 3076, 3082, 3083, 3100, 3108, 3109, 3115, 3116, 3121, 3137, 3140, 3144, 3148, 3149, 3170, 3171, 3172, 3180, 3186, 3187, 3195, 3196, 3202, 3203, 3204, 3217, 3220, 3221, 3222, 3228, 3234, 3235, 3236, 3244, 3249, 3260, 3265, 3268, 3281, 3288, 3289, 3290, 3291, 3292, 3293, 3300, 3308, 3332, 3342, 3352, 3356, 3360, 3361, 3362, 3363, 3364, 3372, 3377, 3396, 3402, 3403, 3404, 3405, 3409, 3416, 3426, 3427, 3428, 3435, 3436, 3437, 3460, 3473, 3484, 3490, 3491, 3492, 3500, 3504, 3505, 3506, 3507, 3512, 3515, 3516, 3521, 3524, 3542, 3543, 3544, 3545, 3546, 3547, 3556, 3564, 3580, 3581, 3588, 3612, 3620, 3627, 3628, 3633, 3649, 3652, 3658, 3659, 3665, 3670, 3681, 3682, 3683, 3684, 3691, 3692, 3700, 3701, 3702, 3708, 3716, 3729, 3740, 3748, 3756, 3757, 3761, 3772, 3780, 3793, 3800, 3812, 3819, 3820, 3832, 3835, 3836, 3844, 3852, 3853, 3868, 3873, 3874, 3875, 3876, 3884, 3889, 3896, 3897, 3898, 3899, 3908, 3938, 3939, 3940, 3948, 3972, 3982, 3983, 3984, 3985, 3986, 3987, 3988, 3989, 3990, 3991, 3992, 3996, 4004, 4012, 4013, 4017, 4024, 4025, 4028, 4029, 4033, 4036, 4068, 4069, 4076, 4077, 4088, 4100, 4106, 4107, 4108, 4109, 4124, 4132, 4140, 4145, 4152, 4153, 4154, 4155, 4161, 4164, 4170, 4171, 4193, 4194, 4195, 4196, 4197, 4204, 4220, 4226, 4227, 4228, 4241, 4248, 4252, 4260, 4268, 4273, 4284, 4289, 4292, 4296, 4305, 4312, 4324, 4332, 4353, 4356, 4380, 4381, 4385, 4386, 4387, 4388, 4396, 4401, 4410, 4411, 4420, 4450, 4451, 4452, 4456, 4457, 4460, 4463, 4468, 4469, 4481, 4482, 4483, 4484, 4485, 4486, 4496, 4497, 4498, 4499, 4508, 4514, 4515, 4516, 4524, 4525, 4528, 4529, 4530, 4531, 4536, 4540, 4545, 4548, 4554, 4555, 4568, 4580, 4588, 4604, 4612, 4636, 4644, 4652, 4657, 4666, 4667, 4673, 4674, 4675, 4676, 4682, 4683, 4689, 4706, 4707, 4708, 4716, 4722, 4723, 4724, 4725, 4726, 4727, 4728, 4729, 4732, 4740, 4753, 4756, 4757, 4758, 4764, 4770, 4771, 4772, 4780, 4785, 4796, 4804, 4817, 4836, 4844, 4860, 4865, 4868, 4876, 4877, 4892, 4898, 4899, 4900, 4907, 4908, 4913, 4920, 4921, 4922, 4923, 4932, 4936, 4937, 4938, 4939, 4940, 4941, 4945, 4962, 4963, 4964, 4971, 4972, 4973, 4996, 5009, 5020, 5021, 5028, 5036, 5040, 5041, 5042, 5043, 5052, 5057, 5060, 5066, 5067, 5092, 5100, 5101, 5108, 5109, 5112, 5124, 5130, 5131, 5137, 5148, 5156, 5157, 5163, 5164, 5169, 5185, 5188, 5196, 5197, 5206, 5218, 5219, 5220, 5228, 5244, 5250, 5251, 5252, 5265, 5268, 5269, 5270, 5276, 5282, 5283, 5284, 5291, 5292, 5297, 5308, 5313, 5314, 5315, 5316, 5317, 5318, 5319, 5320, 5321, 5322, 5323, 5329, 5348, 5356, 5364, 5365, 5372, 5373, 5377, 5380, 5404, 5410, 5411, 5412, 5413, 5420, 5425, 5436, 5437, 5444, 5474, 5475, 5476, 5483, 5484, 5508, 5520, 5521, 5522, 5523, 5532, 5537, 5538, 5539, 5540, 5548, 5549, 5552, 5553, 5554, 5555, 5560, 5563, 5564, 5572, 5590, 5591, 5592, 5596, 5597, 5604, 5612, 5634, 5635, 5636, 5637, 5660, 5665, 5668, 5669, 5675, 5676, 5681, 5697, 5700, 5706, 5707, 5713, 5729, 5730, 5731, 5732, 5740, 5741, 5748, 5749, 5750, 5756, 5764, 5777, 5780, 5781, 5782, 5788, 5794, 5795, 5796, 5804, 5808, 5809, 5810, 5811, 5819, 5820, 5821, 5828, 5841, 5846, 5847, 5848, 5849, 5850, 5851, 5860, 5868, 5880, 5884, 5892, 5916, 5922, 5923, 5924, 5932, 5937, 5940, 5941, 5956, 5974, 5975, 5976, 5980, 5981, 5982, 5986, 5987, 5988, 5996, 6018, 6019, 6020, 6021, 6033, 6036, 6037, 6038, 6039, 6040, 6044, 6045, 6049, 6050, 6051, 6052, 6059, 6060, 6061, 6065, 6072, 6073, 6076, 6084, 6090, 6091, 6102, 6106, 6107, 6116, 6117, 6124, 6125, 6134, 6148, 6164, 6165, 6166, 6172, 6180, 6188, 6193, 6209, 6212, 6220, 6221, 6230, 6231, 6232, 6242, 6243, 6244, 6252, 6267, 6268, 6274, 6275, 6276, 6288, 6289, 6290, 6291, 6296, 6297, 6298, 6299, 6300, 6305, 6308, 6316, 6321, 6332, 6337, 6340, 6344, 6353, 6360, 6372, 6380, 6390, 6404, 6428, 6434, 6435, 6436, 6444, 6449, 6458, 6459, 6468, 6474, 6475, 6481, 6498, 6499, 6500, 6508, 6509, 6530, 6531, 6532, 6533, 6545, 6556, 6561, 6562, 6563, 6564, 6565, 6572, 6573, 6576, 6577, 6578, 6579, 6580, 6581, 6582, 6583, 6584, 6588, 6593, 6596, 6616, 6628, 6636, 6652, 6660, 6684, 6692, 6699, 6700, 6704, 6705, 6706, 6707, 6720, 6721, 6722, 6723, 6724, 6730, 6731, 6737, 6754, 6755, 6756, 6764, 6780, 6781, 6788, 6789, 6801, 6804, 6805, 6806, 6812, 6817, 6818, 6819, 6820, 6828, 6832, 6833, 6834, 6835, 6840, 6844, 6849, 6852, 6865, 6870, 6876, 6877, 6884, 6892, 6908, 6913, 6916, 6929, 6940, 6946, 6947, 6948, 6956, 6961, 6980, 6986, 6987, 6993, 7000, 7010, 7011, 7012, 7019, 7020, 7024, 7025, 7026, 7027, 7030, 7042, 7043, 7044, 7045, 7057, 7068, 7076, 7083, 7084, 7085, 7086, 7087, 7088, 7089, 7090, 7091, 7092, 7093, 7094, 7095, 7096, 7097, 7100, 7105, 7108, 7140, 7148, 7153, 7164, 7169, 7172, 7196, 7204, 7212, 7217, 7233, 7236, 7249, 7254, 7266, 7267, 7268, 7276, 7291, 7292, 7298, 7299, 7300, 7313, 7316, 7317, 7318, 7324, 7330, 7331, 7332, 7340, 7345, 7356, 7361, 7362, 7363, 7364, 7377, 7382, 7383, 7384, 7385, 7386, 7387, 7396, 7404, 7412, 7413, 7416, 7428, 7452, 7453, 7457, 7458, 7459, 7460, 7461, 7468, 7473, 7492, 7512, 7516, 7517, 7522, 7523, 7524, 7532, 7533, 7553, 7556, 7569, 7580, 7586, 7587, 7588, 7596, 7600, 7601, 7602, 7603, 7608, 7611, 7612, 7617, 7620, 7638, 7639, 7640, 7652, 7653, 7659, 7660, 7664, 7665, 7666, 7667, 7670, 7684, 7708, 7716, 7724, 7729, 7738, 7739, 7745, 7746, 7747, 7748, 7754, 7755, 7761, 7778, 7779, 7780, 7788, 7794, 7795, 7796, 7797, 7798, 7799, 7800, 7801, 7804, 7812, 7825, 7836, 7837, 7841, 7844, 7851, 7852, 7853, 7857, 7868, 7876, 7889, 7896, 7908, 7916, 7921, 7932, 7940, 7964, 7968, 7969, 7970, 7971, 7972, 7976, 7977, 7978, 7979, 7980, 7981, 7982, 7983, 7984, 7985, 7986, 7987, 7994, 7995, 8004, 8024, 8028, 8029, 8034, 8035, 8036, 8044, 8045, 8048, 8049, 8050, 8051, 8052, 8053, 8060, 8061, 8065, 8066, 8067, 8068, 8069, 8081, 8092, 8097, 8100, 8108, 8113, 8120, 8121, 8124, 8132, 8136, 8140, 8141, 8156, 8157, 8164, 8172, 8178, 8179, 8188, 8189, 8196, 8212, 8213, 8214, 8220, 8228, 8236, 8241, 8257, 8260, 8290, 8291, 8292, 8300, 8306, 8307, 8308, 8309, 8310, 8316, 8322, 8323, 8324, 8325, 8337, 8340, 8341, 8342, 8348, 8356, 8364, 8369, 8380, 8385, 8386, 8387, 8388, 8389, 8390, 8394, 8395, 8396, 8397, 8401, 8420, 8427, 8428, 8449, 8452, 8458, 8459, 8476, 8477, 8481, 8482, 8483, 8484, 8492, 8496, 8497, 8498, 8499, 8506, 8507, 8516, 8520, 8546, 8547, 8548, 8556, 8557, 8570, 8571, 8578, 8579, 8580, 8581, 8592, 8593, 8594, 8595, 8604, 8610, 8611, 8612, 8613, 8620, 8624, 8625, 8626, 8627, 8632, 8636, 8641, 8644, 8664, 8676, 8684, 8700, 8706, 8707, 8708, 8732, 8733, 8740, 8741, 8748, 8753, 8764, 8765, 8769, 8770, 8771, 8772, 8773, 8774, 8775, 8776, 8777, 8778, 8779, 8785, 8802, 8803, 8804, 8811, 8812, 8813, 8820, 8821, 8822, 8828, 8836, 8837, 8849, 8860, 8868, 8869, 8875, 8876, 8881, 8892, 8900, 8912, 8913, 8914, 8915, 8916, 8917, 8926, 8932, 8940, 8956, 8961, 8962, 8963, 8964, 8972, 8973, 8974, 8975, 8988, 8994, 8995, 8996, 9004, 9009, 9028, 9034, 9035, 9041, 9052, 9053, 9058, 9059, 9060, 9068, 9069, 9072, 9073, 9074, 9075, 9089, 9090, 9091, 9092, 9093, 9105, 9108, 9109, 9110, 9111, 9112, 9115, 9116, 9121, 9124, 9125, 9132, 9133, 9136, 9137, 9138, 9139, 9148, 9153, 9156, 9160, 9169, 9178, 9179, 9188, 9189, 9195, 9196, 9217, 9220, 9244, 9252, 9260, 9265, 9281, 9284, 9314, 9315, 9316, 9324, 9332, 9333, 9334, 9340, 9346, 9347, 9348, 9361, 9364, 9365, 9366, 9367, 9368, 9372, 9378, 9379, 9380, 9388, 9393, 9403, 9404, 9409, 9412, 9425, 9444, 9448, 9452, 9456, 9457, 9458, 9459, 9460, 9461, 9473, 9476, 9480, 9500, 9506, 9507, 9508, 9509, 9516, 9521, 9537, 9540, 9546, 9547, 9553, 9570, 9571, 9572, 9580, 9594, 9595, 9604, 9617, 9628, 9634, 9635, 9636, 9643, 9644, 9649, 9660, 9665, 9668, 9672, 9688, 9700, 9708, 9720, 9730, 9731, 9732, 9733, 9756, 9764, 9765, 9772, 9777, 9793, 9796, 9802, 9803, 9809, 9814, 9815, 9816, 9826, 9827, 9828, 9836, 9842, 9843, 9844, 9845, 9846, 9847, 9848, 9849, 9852, 9860, 9861, 9872, 9873, 9874, 9875, 9876, 9877, 9878, 9884, 9889, 9890, 9891, 9892, 9893, 9900, 9901, 9905, 9915, 9916, 9924, 9937, 9942, 9943, 9944, 9948, 9949, 9956, 9964, 9979, 9980, 9988]
1782
N=10000 quad_values=[] for i in srange(N): if h(i)==h(i+1) and h(i)==h(i+2) and h(i)==h(i+3): quad_values.append(i) print(quad_values) len(quad_values) 
       
[98, 99, 130, 131, 290, 291, 314, 354, 355, 386, 387, 388, 418, 419,
514, 515, 586, 610, 611, 628, 629, 747, 780, 802, 803, 840, 841, 842,
866, 867, 943, 944, 945, 946, 996, 1034, 1121, 1122, 1123, 1132, 1154,
1155, 1172, 1173, 1179, 1186, 1187, 1195, 1314, 1315, 1378, 1379, 1442,
1443, 1494, 1495, 1496, 1497, 1498, 1538, 1539, 1572, 1610, 1634, 1635,
1644, 1680, 1681, 1682, 1683, 1684, 1685, 1698, 1699, 1700, 1771, 1788,
1826, 1827, 1835, 1850, 1890, 1891, 1922, 1923, 1924, 1991, 1992, 1993,
1994, 1995, 1996, 2050, 2051, 2052, 2068, 2069, 2082, 2083, 2146, 2147,
2178, 2179, 2241, 2242, 2243, 2268, 2337, 2338, 2339, 2358, 2359, 2360,
2361, 2362, 2378, 2402, 2403, 2434, 2435, 2436, 2466, 2467, 2468, 2514,
2562, 2563, 2596, 2603, 2634, 2657, 2658, 2659, 2684, 2716, 2795, 2796,
2850, 2851, 2874, 2890, 2914, 2915, 2923, 2987, 2988, 2989, 2990, 2991,
2992, 2993, 2994, 2995, 2996, 2997, 3018, 3051, 3067, 3082, 3108, 3115,
3148, 3170, 3171, 3186, 3195, 3202, 3203, 3220, 3221, 3234, 3235, 3288,
3289, 3290, 3291, 3292, 3360, 3361, 3362, 3363, 3402, 3403, 3404, 3426,
3427, 3435, 3436, 3490, 3491, 3504, 3505, 3506, 3515, 3542, 3543, 3544,
3545, 3546, 3580, 3627, 3658, 3681, 3682, 3683, 3691, 3700, 3701, 3756,
3819, 3835, 3852, 3873, 3874, 3875, 3896, 3897, 3898, 3938, 3939, 3982,
3983, 3984, 3985, 3986, 3987, 3988, 3989, 3990, 3991, 4012, 4024, 4028,
4068, 4076, 4106, 4107, 4108, 4152, 4153, 4154, 4170, 4193, 4194, 4195,
4196, 4226, 4227, 4380, 4385, 4386, 4387, 4410, 4450, 4451, 4456, 4468,
4481, 4482, 4483, 4484, 4485, 4496, 4497, 4498, 4514, 4515, 4524, 4528,
4529, 4530, 4554, 4666, 4673, 4674, 4675, 4682, 4706, 4707, 4722, 4723,
4724, 4725, 4726, 4727, 4728, 4756, 4757, 4770, 4771, 4876, 4898, 4899,
4907, 4920, 4921, 4922, 4936, 4937, 4938, 4939, 4940, 4962, 4963, 4971,
4972, 5020, 5040, 5041, 5042, 5066, 5100, 5108, 5130, 5156, 5163, 5196,
5218, 5219, 5250, 5251, 5268, 5269, 5282, 5283, 5291, 5313, 5314, 5315,
5316, 5317, 5318, 5319, 5320, 5321, 5322, 5364, 5372, 5410, 5411, 5412,
5436, 5474, 5475, 5483, 5520, 5521, 5522, 5537, 5538, 5539, 5548, 5552,
5553, 5554, 5563, 5590, 5591, 5596, 5634, 5635, 5636, 5668, 5675, 5706,
5729, 5730, 5731, 5740, 5748, 5749, 5780, 5781, 5794, 5795, 5808, 5809,
5810, 5819, 5820, 5846, 5847, 5848, 5849, 5850, 5922, 5923, 5940, 5974,
5975, 5980, 5981, 5986, 5987, 6018, 6019, 6020, 6036, 6037, 6038, 6039,
6044, 6049, 6050, 6051, 6059, 6060, 6072, 6090, 6106, 6116, 6124, 6164,
6165, 6220, 6230, 6231, 6242, 6243, 6267, 6274, 6275, 6288, 6289, 6290,
6296, 6297, 6298, 6299, 6434, 6435, 6458, 6474, 6498, 6499, 6508, 6530,
6531, 6532, 6561, 6562, 6563, 6564, 6572, 6576, 6577, 6578, 6579, 6580,
6581, 6582, 6583, 6699, 6704, 6705, 6706, 6720, 6721, 6722, 6723, 6730,
6754, 6755, 6780, 6788, 6804, 6805, 6817, 6818, 6819, 6832, 6833, 6834,
6876, 6946, 6947, 6986, 7010, 7011, 7019, 7024, 7025, 7026, 7042, 7043,
7044, 7083, 7084, 7085, 7086, 7087, 7088, 7089, 7090, 7091, 7092, 7093,
7094, 7095, 7096, 7266, 7267, 7291, 7298, 7299, 7316, 7317, 7330, 7331,
7361, 7362, 7363, 7382, 7383, 7384, 7385, 7386, 7412, 7452, 7457, 7458,
7459, 7460, 7516, 7522, 7523, 7532, 7586, 7587, 7600, 7601, 7602, 7611,
7638, 7639, 7652, 7659, 7664, 7665, 7666, 7738, 7745, 7746, 7747, 7754,
7778, 7779, 7794, 7795, 7796, 7797, 7798, 7799, 7800, 7836, 7851, 7852,
7968, 7969, 7970, 7971, 7976, 7977, 7978, 7979, 7980, 7981, 7982, 7983,
7984, 7985, 7986, 7994, 8028, 8034, 8035, 8044, 8048, 8049, 8050, 8051,
8052, 8060, 8065, 8066, 8067, 8068, 8120, 8140, 8156, 8178, 8188, 8212,
8213, 8290, 8291, 8306, 8307, 8308, 8309, 8322, 8323, 8324, 8340, 8341,
8385, 8386, 8387, 8388, 8389, 8394, 8395, 8396, 8427, 8458, 8476, 8481,
8482, 8483, 8496, 8497, 8498, 8506, 8546, 8547, 8556, 8570, 8578, 8579,
8580, 8592, 8593, 8594, 8610, 8611, 8612, 8624, 8625, 8626, 8706, 8707,
8732, 8740, 8764, 8769, 8770, 8771, 8772, 8773, 8774, 8775, 8776, 8777,
8778, 8802, 8803, 8811, 8812, 8820, 8821, 8836, 8868, 8875, 8912, 8913,
8914, 8915, 8916, 8961, 8962, 8963, 8972, 8973, 8974, 8994, 8995, 9034,
9052, 9058, 9059, 9068, 9072, 9073, 9074, 9089, 9090, 9091, 9092, 9108,
9109, 9110, 9111, 9115, 9124, 9132, 9136, 9137, 9138, 9178, 9188, 9195,
9314, 9315, 9332, 9333, 9346, 9347, 9364, 9365, 9366, 9367, 9378, 9379,
9403, 9456, 9457, 9458, 9459, 9460, 9506, 9507, 9508, 9546, 9570, 9571,
9594, 9634, 9635, 9643, 9730, 9731, 9732, 9764, 9802, 9814, 9815, 9826,
9827, 9842, 9843, 9844, 9845, 9846, 9847, 9848, 9860, 9872, 9873, 9874,
9875, 9876, 9877, 9889, 9890, 9891, 9892, 9900, 9915, 9942, 9943, 9948,
9979]
762
[98, 99, 130, 131, 290, 291, 314, 354, 355, 386, 387, 388, 418, 419, 514, 515, 586, 610, 611, 628, 629, 747, 780, 802, 803, 840, 841, 842, 866, 867, 943, 944, 945, 946, 996, 1034, 1121, 1122, 1123, 1132, 1154, 1155, 1172, 1173, 1179, 1186, 1187, 1195, 1314, 1315, 1378, 1379, 1442, 1443, 1494, 1495, 1496, 1497, 1498, 1538, 1539, 1572, 1610, 1634, 1635, 1644, 1680, 1681, 1682, 1683, 1684, 1685, 1698, 1699, 1700, 1771, 1788, 1826, 1827, 1835, 1850, 1890, 1891, 1922, 1923, 1924, 1991, 1992, 1993, 1994, 1995, 1996, 2050, 2051, 2052, 2068, 2069, 2082, 2083, 2146, 2147, 2178, 2179, 2241, 2242, 2243, 2268, 2337, 2338, 2339, 2358, 2359, 2360, 2361, 2362, 2378, 2402, 2403, 2434, 2435, 2436, 2466, 2467, 2468, 2514, 2562, 2563, 2596, 2603, 2634, 2657, 2658, 2659, 2684, 2716, 2795, 2796, 2850, 2851, 2874, 2890, 2914, 2915, 2923, 2987, 2988, 2989, 2990, 2991, 2992, 2993, 2994, 2995, 2996, 2997, 3018, 3051, 3067, 3082, 3108, 3115, 3148, 3170, 3171, 3186, 3195, 3202, 3203, 3220, 3221, 3234, 3235, 3288, 3289, 3290, 3291, 3292, 3360, 3361, 3362, 3363, 3402, 3403, 3404, 3426, 3427, 3435, 3436, 3490, 3491, 3504, 3505, 3506, 3515, 3542, 3543, 3544, 3545, 3546, 3580, 3627, 3658, 3681, 3682, 3683, 3691, 3700, 3701, 3756, 3819, 3835, 3852, 3873, 3874, 3875, 3896, 3897, 3898, 3938, 3939, 3982, 3983, 3984, 3985, 3986, 3987, 3988, 3989, 3990, 3991, 4012, 4024, 4028, 4068, 4076, 4106, 4107, 4108, 4152, 4153, 4154, 4170, 4193, 4194, 4195, 4196, 4226, 4227, 4380, 4385, 4386, 4387, 4410, 4450, 4451, 4456, 4468, 4481, 4482, 4483, 4484, 4485, 4496, 4497, 4498, 4514, 4515, 4524, 4528, 4529, 4530, 4554, 4666, 4673, 4674, 4675, 4682, 4706, 4707, 4722, 4723, 4724, 4725, 4726, 4727, 4728, 4756, 4757, 4770, 4771, 4876, 4898, 4899, 4907, 4920, 4921, 4922, 4936, 4937, 4938, 4939, 4940, 4962, 4963, 4971, 4972, 5020, 5040, 5041, 5042, 5066, 5100, 5108, 5130, 5156, 5163, 5196, 5218, 5219, 5250, 5251, 5268, 5269, 5282, 5283, 5291, 5313, 5314, 5315, 5316, 5317, 5318, 5319, 5320, 5321, 5322, 5364, 5372, 5410, 5411, 5412, 5436, 5474, 5475, 5483, 5520, 5521, 5522, 5537, 5538, 5539, 5548, 5552, 5553, 5554, 5563, 5590, 5591, 5596, 5634, 5635, 5636, 5668, 5675, 5706, 5729, 5730, 5731, 5740, 5748, 5749, 5780, 5781, 5794, 5795, 5808, 5809, 5810, 5819, 5820, 5846, 5847, 5848, 5849, 5850, 5922, 5923, 5940, 5974, 5975, 5980, 5981, 5986, 5987, 6018, 6019, 6020, 6036, 6037, 6038, 6039, 6044, 6049, 6050, 6051, 6059, 6060, 6072, 6090, 6106, 6116, 6124, 6164, 6165, 6220, 6230, 6231, 6242, 6243, 6267, 6274, 6275, 6288, 6289, 6290, 6296, 6297, 6298, 6299, 6434, 6435, 6458, 6474, 6498, 6499, 6508, 6530, 6531, 6532, 6561, 6562, 6563, 6564, 6572, 6576, 6577, 6578, 6579, 6580, 6581, 6582, 6583, 6699, 6704, 6705, 6706, 6720, 6721, 6722, 6723, 6730, 6754, 6755, 6780, 6788, 6804, 6805, 6817, 6818, 6819, 6832, 6833, 6834, 6876, 6946, 6947, 6986, 7010, 7011, 7019, 7024, 7025, 7026, 7042, 7043, 7044, 7083, 7084, 7085, 7086, 7087, 7088, 7089, 7090, 7091, 7092, 7093, 7094, 7095, 7096, 7266, 7267, 7291, 7298, 7299, 7316, 7317, 7330, 7331, 7361, 7362, 7363, 7382, 7383, 7384, 7385, 7386, 7412, 7452, 7457, 7458, 7459, 7460, 7516, 7522, 7523, 7532, 7586, 7587, 7600, 7601, 7602, 7611, 7638, 7639, 7652, 7659, 7664, 7665, 7666, 7738, 7745, 7746, 7747, 7754, 7778, 7779, 7794, 7795, 7796, 7797, 7798, 7799, 7800, 7836, 7851, 7852, 7968, 7969, 7970, 7971, 7976, 7977, 7978, 7979, 7980, 7981, 7982, 7983, 7984, 7985, 7986, 7994, 8028, 8034, 8035, 8044, 8048, 8049, 8050, 8051, 8052, 8060, 8065, 8066, 8067, 8068, 8120, 8140, 8156, 8178, 8188, 8212, 8213, 8290, 8291, 8306, 8307, 8308, 8309, 8322, 8323, 8324, 8340, 8341, 8385, 8386, 8387, 8388, 8389, 8394, 8395, 8396, 8427, 8458, 8476, 8481, 8482, 8483, 8496, 8497, 8498, 8506, 8546, 8547, 8556, 8570, 8578, 8579, 8580, 8592, 8593, 8594, 8610, 8611, 8612, 8624, 8625, 8626, 8706, 8707, 8732, 8740, 8764, 8769, 8770, 8771, 8772, 8773, 8774, 8775, 8776, 8777, 8778, 8802, 8803, 8811, 8812, 8820, 8821, 8836, 8868, 8875, 8912, 8913, 8914, 8915, 8916, 8961, 8962, 8963, 8972, 8973, 8974, 8994, 8995, 9034, 9052, 9058, 9059, 9068, 9072, 9073, 9074, 9089, 9090, 9091, 9092, 9108, 9109, 9110, 9111, 9115, 9124, 9132, 9136, 9137, 9138, 9178, 9188, 9195, 9314, 9315, 9332, 9333, 9346, 9347, 9364, 9365, 9366, 9367, 9378, 9379, 9403, 9456, 9457, 9458, 9459, 9460, 9506, 9507, 9508, 9546, 9570, 9571, 9594, 9634, 9635, 9643, 9730, 9731, 9732, 9764, 9802, 9814, 9815, 9826, 9827, 9842, 9843, 9844, 9845, 9846, 9847, 9848, 9860, 9872, 9873, 9874, 9875, 9876, 9877, 9889, 9890, 9891, 9892, 9900, 9915, 9942, 9943, 9948, 9979]
762
N=10000 quin_values=[] for i in srange(N): if h(i)==h(i+1) and h(i)==h(i+2) and h(i)==h(i+3) and h(i)==h(i+4): quin_values.append(i) #print(quin_values) len(quin_values) 
       
410
410
hail[:10] 
       
[[1, 0],
 [2, 1],
 [3, 7],
 [4, 2],
 [5, 5],
 [6, 8],
 [7, 16],
 [8, 3],
 [9, 19],
 [10, 6]]
[[1, 0],
 [2, 1],
 [3, 7],
 [4, 2],
 [5, 5],
 [6, 8],
 [7, 16],
 [8, 3],
 [9, 19],
 [10, 6]]
N=100000 six_values=[] for i in srange(N-2): #if h(i)==h(i+1) and h(i)==h(i+2) and h(i)==h(i+3) and h(i)==h(i+4): if hail[i][1] == hail[i+1][1] and hail[i][1] == hail[i+2][1] and hail[i][1]==hail[i+3][1] and hail[i][1]==hail[i+4][1] and hail[i][1]==hail[i+5][1]: six_values.append(i) #print(six_values) len(six_values) 
       
3127
3127
       
99998
99998

It *seems* to be the case that there are lots of consecutive integers which have the same value for the hailstone function.

Can we explain, heuristically, why this ought to be the case?

How many $n$ are such that $h(n)>n$?

What about other functions of $n$?  How often is $h(n)>\sqrt{n}$?

How should "random" integers behave?  How long for a number which behaves randomly to reach 4,2,1?


bigger_than_n=[] for i in hail: if i[1]>i[0]: bigger_than_n.append(i) print(bigger_than_n) 
       
[[3, 7], [6, 8], [7, 16], [9, 19], [11, 14], [14, 17], [15, 17], [18,
20], [19, 20], [27, 111], [31, 106], [41, 109], [47, 104], [54, 112],
[55, 112], [62, 107], [63, 107], [71, 102], [73, 115], [82, 110], [83,
110], [91, 92], [94, 105], [95, 105], [97, 118], [108, 113], [109, 113],
[110, 113]]
[[3, 7], [6, 8], [7, 16], [9, 19], [11, 14], [14, 17], [15, 17], [18, 20], [19, 20], [27, 111], [31, 106], [41, 109], [47, 104], [54, 112], [55, 112], [62, 107], [63, 107], [71, 102], [73, 115], [82, 110], [83, 110], [91, 92], [94, 105], [95, 105], [97, 118], [108, 113], [109, 113], [110, 113]]
bigger_than_root_n=[] for i in hail: if i[1]^2>i[0]: bigger_than_root_n.append(i) len(bigger_than_root_n) 
       
12077
12077