cp's OEIS Frontend

A375519 Number of positive integers with Pisano period equal to n.

%I A375519 #19 Aug 28 2024 16:37:04
%S A375519 1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,2,0,3,0,2,0,1,0,10,0,1,0,2,0,8,0,4,
%T A375519 0,1,0,9,0,1,0,11,0,8,0,2,0,3,0,55,0,6,0,2,0,6,0,11,0,3,0,49,0,1,0,8,
%U A375519 0,8,0,2,0,13,0,133,0,1,0,6,0,20,0,46,0,1,0,49,0,3,0,27,0,81,0,4,0,10,260,0,2,0,38
%N A375519 Number of positive integers with Pisano period equal to n.
%C A375519 See also A375089, which is the main entry.
%C A375519 [This was the version of A375089 that was originally submitted. I think both belong in the OEIS. - _N. J. A. Sloane_, Aug 28 2024]
%F A375519 a(2n) = A375089(n). - _Chai Wah Wu_, Aug 28 2024
%o A375519 (Python)
%o A375519 from functools import lru_cache
%o A375519 from math import gcd, lcm
%o A375519 from sympy import factorint, divisors, fibonacci
%o A375519 def A375519(n):
%o A375519     @lru_cache(maxsize=None)
%o A375519     def A001175(n):
%o A375519         if n == 1:
%o A375519             return 1
%o A375519         f = factorint(n).items()
%o A375519         if len(f) > 1:
%o A375519             return lcm(*(A001175(a**b) for a,b in f))
%o A375519         else:
%o A375519             k,x = 1, (1,1)
%o A375519             while x != (0,1):
%o A375519                 k += 1
%o A375519                 x = (x[1], (x[0]+x[1]) % n)
%o A375519             return k
%o A375519     a, b = fibonacci(n+1), fibonacci(n)
%o A375519     return sum(1 for d in divisors(gcd(a-1,b),generator=True) if A001175(d)==n) # _Chai Wah Wu_, Aug 28 2024
%Y A375519 Cf. A001175, A375089.
%K A375519 nonn
%O A375519 1,18
%A A375519 _Oliver Lippard_ and _Brennan G. Benfield_, Jul 29 2024