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

1,2

Links

Table of n, a(n) for n=1..48.

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}]

Prog

(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

Crossrefs

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

Sequence in context: A000860 A222397 A334257 * A097382 A266063 A282284

Adjacent sequences: A193991 A193992 A193993 * A193995 A193996 A193997

Keyword

nonn

Author

T. D. Noe, Aug 18 2011

Status

approved