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

%I A193994 #12 Feb 27 2022 11:52:29
%S A193994 1,4,35,7,156,70,400,12,45,624,1580,61,2380,1600,5460,18,5220,33,684,
%T A193994 1092,14000,6320,523,52,185,9520,48,2800,2465,10920,6075,22,55300,
%U A193994 20880,62400,28,52060,464,83300,1872,70180,28000,1903,11060,7020,1046,22,79
%N A193994 Number of zeros in the period of Fibonacci 5-step sequence A001591 mod n.
%t A193994 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 A193994 (Python)
%o A193994 from itertools import count
%o A193994 def A193994(n):
%o A193994     a = b = (0,)*4+(1 % n,)
%o A193994     c, s = 0, 1 % n
%o A193994     for m in count(1):
%o A193994         b, s = b[1:] + (s,), (s+s-b[0])% n
%o A193994         c += int(s==0)
%o A193994         if a == b:
%o A193994             return c # _Chai Wah Wu_, Feb 22-27 2022
%Y A193994 Cf. A106303 (period of Fibonacci 5-step sequence).
%K A193994 nonn
%O A193994 1,2
%A A193994 _T. D. Noe_, Aug 18 2011