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A193994
Number of zeros in the period of Fibonacci 5-step sequence A001591 mod n.
1
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
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
KEYWORD
nonn
AUTHOR
T. D. Noe, Aug 18 2011
STATUS
approved