%I #12 Feb 27 2022 11:52:29

%S 1,4,35,7,156,70,400,12,45,624,1580,61,2380,1600,5460,18,5220,33,684,

%T 1092,14000,6320,523,52,185,9520,48,2800,2465,10920,6075,22,55300,

%U 20880,62400,28,52060,464,83300,1872,70180,28000,1903,11060,7020,1046,22,79

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

%t 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}]

%o (Python)

%o from itertools import count

%o def A193994(n):

%o a = b = (0,)*4+(1 % n,)

%o c, s = 0, 1 % n

%o for m in count(1):

%o b, s = b[1:] + (s,), (s+s-b[0])% n

%o c += int(s==0)

%o if a == b:

%o return c # _Chai Wah Wu_, Feb 22-27 2022

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

%K nonn

%O 1,2

%A _T. D. Noe_, Aug 18 2011