2023.02.10 Math 3600 3n+1 Peaks

223 days ago by calkin

We will work with both f(n) (3n+1) and g(n) (3n+1)/2.  We'll compute which numbers are peaks.
def f(n): if n<1 or (type(n)==Integer)==False: return("Please input a positive integer") elif is_even(n): return(Integer(n/2)) else: return(3*n+1) def g(n): if n<1 or (type(n)==Integer)==False: return("Please input a positive integer") elif is_even(n): return(Integer(n/2)) else: return(Integer((3*n+1)/2)) 
       
def is_f_peak(m): a=m while a>1 and a<m+1: a=f(a) if a==1: return(True) else: return(False) def is_g_peak(m): a=m while a>1 and a<m+1: a=g(a) if a==1: return(True) else: return(False) 
       
is_f_peak(4) 
        
True
True
is_f_peak(5) 
        
False
False
fpeaks=[] for i in srange(2,1000000): if is_f_peak(i): fpeaks.append(i) 
       
len(fpeaks) 
        
143290
143290
gpeaks=[] for i in srange(2,1000000): if is_g_peak(i): gpeaks.append(i) len(gpeaks) 
        
287336
287336
fpeaks[-10:] 
        
[999940,
 999944,
 999952,
 999956,
 999960,
 999968,
 999976,
 999984,
 999988,
 999992]
[999940,
 999944,
 999952,
 999956,
 999960,
 999968,
 999976,
 999984,
 999988,
 999992]
gpeaks[-20:] 
        
[999938,
 999940,
 999944,
 999946,
 999948,
 999952,
 999956,
 999960,
 999962,
 999964,
 999968,
 999970,
 999976,
 999978,
 999980,
 999984,
 999986,
 999988,
 999992,
 999994]
[999938,
 999940,
 999944,
 999946,
 999948,
 999952,
 999956,
 999960,
 999962,
 999964,
 999968,
 999970,
 999976,
 999978,
 999980,
 999984,
 999986,
 999988,
 999992,
 999994]
fpeaks[:20] 
        
[2, 4, 8, 16, 20, 24, 32, 40, 48, 52, 56, 64, 68, 72, 80, 84, 88, 96,
100, 104]
[2, 4, 8, 16, 20, 24, 32, 40, 48, 52, 56, 64, 68, 72, 80, 84, 88, 96, 100, 104]
print(gpeaks[:40]) 
        
[2, 4, 8, 10, 12, 16, 20, 24, 26, 28, 32, 34, 36, 40, 42, 44, 48, 50,
52, 56, 58, 64, 66, 68, 72, 74, 76, 80, 84, 88, 90, 92, 96, 98, 100,
104, 106, 112, 114, 116]
[2, 4, 8, 10, 12, 16, 20, 24, 26, 28, 32, 34, 36, 40, 42, 44, 48, 50, 52, 56, 58, 64, 66, 68, 72, 74, 76, 80, 84, 88, 90, 92, 96, 98, 100, 104, 106, 112, 114, 116]