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%I #15 Feb 16 2025 08:32:57
%S 3,8,4,16,10,28,36,18,48,14,30,76,40,88,32,108,58,60,136,70,148,78,
%T 168,44,196,50,208,72,108,76,256,130,276,46,148,50,316,328,336,348,
%U 178,90,190,388,396,22,42,448,456,114,52,238,240,250,516,176,268,270,556,56
%N Period of the Lucas sequence A000032 mod prime(n).
%C This sequence differs from A060305 at only one position: 3, which corresponds to the prime 5, which is the discriminant of the characteristic polynomial x^2-x-1. We have a(n) < prime(n) for the primes in A038872.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>.
%F a(n) = A106291(prime(n)).
%t n=2; Table[p=Prime[i]; a=Join[Table[ -1, {n-1}], {n}]; a=Mod[a, p]; a0=a; k=0; While[k++; s=Mod[Plus@@a, p]; a=RotateLeft[a]; a[[n]]=s; a!=a0]; k, {i, 70}]
%Y Cf. A060305 (period of Fibonacci numbers mod prime(n)), A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1), A106291.
%K nonn
%O 1,1
%A _T. D. Noe_, May 02 2005