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Code for OEIS sequence A345209
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| """ | |
| Function to calculate terms of OEIS sequence A345209. | |
| """ | |
| from sympy import primefactors | |
| def a345209(n): | |
| """ | |
| Calculate OEIS entry A345209(n) | |
| (Number of Petrie polygons on regular triangular map corresponding to the principal congruence subgroup Γ(n) of the mmodular group) | |
| n: int, >=1 | |
| return: int | |
| """ | |
| # degenerate cases | |
| if n == 1 or n == 2: | |
| return 1 | |
| # calculate index of Γ(n) in Γ (a001766(n), n>=3) | |
| # given by formula ((n^3)/2)*Product_{p | n, p prime} (1-1/p^2), for n>=3. | |
| index = n**3 | |
| for p in primefactors(n): | |
| index *= (p**2 - 1) | |
| index //= p**2 | |
| index //= 2 | |
| # calculate pisano semiperiod (a301759(n), n>=2) | |
| # period of the Fibonacci numbers modulo n up to a sign | |
| sigma = 1 | |
| a, b = 1, 1 | |
| while (a,b) != (0,1) and (a,b) != (0, n - 1): | |
| a, b = b, (a + b) % n | |
| sigma += 1 | |
| # a(n) = index / sigma | |
| # https://doi.org/10.26493/1855-3974.864.e9b, Corollary 7.3 | |
| return index // sigma | |
| """ | |
| # uncomment this block to print 50 sample values | |
| print(",".join([str(a345209(n)) for n in range(1, 51)])) | |
| """ |
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| """ | |
| Script to generate b-file. | |
| """ | |
| from a345209 import a345209 | |
| def b345209(n=1000): | |
| """ | |
| Generate b-file for OEIS entry A345209. | |
| n: int, >=1 | |
| return: None | |
| """ | |
| bfile = "b345209.txt" | |
| with open(bfile, 'w') as f: | |
| f.writelines([f"{i} {a345209(i)}\n" for i in range(1, n+1)]) | |
| b345209() |
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| 1 1 | |
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