A193994 Number of zeros in the period of Fibonacci 5-step sequence A001591 mod n.

1, 4, 35, 7, 156, 70, 400, 12, 45, 624, 1580, 61, 2380, 1600, 5460, 18, 5220, 33, 684, 1092, 14000, 6320, 523, 52, 185, 9520, 48, 2800, 2465, 10920, 6075, 22, 55300, 20880, 62400, 28, 52060, 464, 83300, 1872, 70180, 28000, 1903, 11060, 7020, 1046, 22, 79

Offset: 1

Author

T. D. Noe, Aug 18 2011

Keywords

• nonn

Crossrefs

Cf. A106303 (period of Fibonacci 5-step sequence).

Programs

Mathematica

n = 5; Table[a = Join[{1}, Table[0, {n - 1}]]; a = Mod[a, i]; a0 = a; k = 0; zeros = 0; While[k++; s = Mod[Plus @@ a, i]; a = RotateLeft[a]; If[s == 0, zeros++]; a[[n]] = s; a != a0]; zeros, {i, 100}]

Python

from itertools import count
def A193994(n):
    a = b = (0,)*4+(1 % n,)
    c, s = 0, 1 % n
    for m in count(1):
        b, s = b[1:] + (s,), (s+s-b[0])% n
        c += int(s==0)
        if a == b:
            return c # Chai Wah Wu, Feb 22-27 2022