def isEgyptian(a, b, c, n ):
if (4 * a * b * c) / (a * b + b * c + a * c) == n:
return true
def findEgyptianFractions(n):
results = []
for a in range(1, 1 + ceil(3 * n / 4)):
if (a * 4 - n) != 0:
for b in range(1, 1 + ceil(2 * a * n / (4 * a - n))):
if n != (4 * a * b) / (a + b):
for c in range(1, 1 + ceil(a * b * n / (4 * a * b - a * n - b * n))):
if isEgyptian(a, b, c, n):
if ((c >= b) and (b >= a)):
results.append([a, b, c])
return results
def countEgyptianFractions(n):
count = 0
for a in range(1, 1 + ceil(3 * n / 4)):
if (a * 4 - n) != 0:
for b in range(1, 1 + ceil(2 * a * n / (4 * a - n))):
if n != (4 * a * b) / (a + b):
for c in range(1, 1 + ceil(a * b * n / (4 * a * b - a * n - b * n))):
if isEgyptian(a, b, c, n):
if ((c >= b) and (b >= a)):
count += 1
return count
# Generate Data for growth rate plot
resultsList = []
for n in range(2, 50):
print(n)
resultsList.append([n, countEgyptianFractions(n)])
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 |
def findEgyptianFractionsFaster(n):
results = []
for a in range(ceil((n + 1) / 4), 1 + ceil(3 * n / 4)):
if ((a * 4 - n) != 0) and ((4 * a - n) != 0):
for b in range(ceil(n * a / (4 * a - n)), 1 + ceil(2 * a * n / (4 * a - n))):
if n != (4 * a * b) / (a + b):
for c in range(1, 1 + ceil(a * b * n / (4 * a * b - a * n - b * n))):
if isEgyptian(a, b, c, n):
if ((c >= b) and (b >= a)):
results.append([a, b, c])
return results
def countEgyptianFractionsFaster(n):
count = 0
for a in range(ceil((n + 1) / 4), 1 + ceil(3 * n / 4)):
if ((a * 4 - n) != 0) and ((4 * a - n) != 0):
for b in range(ceil(n * a / (4 * a - n)), 1 + ceil(2 * a * n / (4 * a - n))):
if n != (4 * a * b) / (a + b):
for c in range(1, 1 + ceil(a * b * n / (4 * a * b - a * n - b * n))):
if isEgyptian(a, b, c, n):
if ((c >= b) and (b >= a)):
count += 1
return count
findEgyptianFractionsFaster(4)
[[2, 3, 6], [2, 4, 4], [3, 3, 3]] [[2, 3, 6], [2, 4, 4], [3, 3, 3]] |
# Generate Data for growth rate plot
resultsList = []
for n in range(2, 50):
print(n)
resultsList.append([n, countEgyptianFractionsFaster(n)])
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 |
list_plot(resultsList)
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findEgyptianFractions(4)
[[2, 3, 6], [2, 4, 4], [3, 3, 3]] [[2, 3, 6], [2, 4, 4], [3, 3, 3]] |
print(resultsList)
[[2, 1], [3, 3], [4, 3], [5, 2], [6, 8], [7, 7], [8, 10], [9, 6], [10, 12], [11, 9], [12, 21], [13, 4], [14, 17], [15, 39], [16, 28], [17, 4], [18, 26], [19, 11], [20, 36], [21, 29], [22, 25], [23, 21], [24, 57], [25, 10], [26, 20], [27, 29], [28, 42], [29, 7], [30, 81], [31, 19], [32, 70], [33, 31], [34, 25], [35, 65], [36, 79], [37, 9], [38, 32], [39, 73], [40, 96], [41, 7], [42, 86], [43, 14], [44, 62], [45, 93], [46, 42], [47, 34], [48, 160], [49, 18]] [[2, 1], [3, 3], [4, 3], [5, 2], [6, 8], [7, 7], [8, 10], [9, 6], [10, 12], [11, 9], [12, 21], [13, 4], [14, 17], [15, 39], [16, 28], [17, 4], [18, 26], [19, 11], [20, 36], [21, 29], [22, 25], [23, 21], [24, 57], [25, 10], [26, 20], [27, 29], [28, 42], [29, 7], [30, 81], [31, 19], [32, 70], [33, 31], [34, 25], [35, 65], [36, 79], [37, 9], [38, 32], [39, 73], [40, 96], [41, 7], [42, 86], [43, 14], [44, 62], [45, 93], [46, 42], [47, 34], [48, 160], [49, 18]] |
# Generate Data for growth rate plot
primeResultsList = []
for n in srange(2, 50):
if n.is_prime():
print(n)
primeResultsList.append([n, countEgyptianFractionsFaster(n)])
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 |
# Plot Result
list_plot(resultsList, color='blue') + list_plot(primeResultsList, color='red')
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# Generate Data for growth rate plot
primeResultsList = []
mod1List = []
mod2List = []
mod3List = []
mod4List = []
mod5List = []
mod6List = []
mod7List = []
for n in srange(2, 50):
x = countEgyptianFractionsFaster(n)
print(n)
if n.is_prime():
primeResultsList.append([n, x])
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