A106292 Period of the Lucas sequence A000032 mod prime(n).

3, 8, 4, 16, 10, 28, 36, 18, 48, 14, 30, 76, 40, 88, 32, 108, 58, 60, 136, 70, 148, 78, 168, 44, 196, 50, 208, 72, 108, 76, 256, 130, 276, 46, 148, 50, 316, 328, 336, 348, 178, 90, 190, 388, 396, 22, 42, 448, 456, 114, 52, 238, 240, 250, 516, 176, 268, 270, 556, 56

Offset: 1

Author

T. D. Noe, May 02 2005

Keywords

• nonn

Comments

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.

Links

• Eric Weisstein's World of Mathematics, Fibonacci n-Step Number.

Crossrefs

Cf. A060305 (period of Fibonacci numbers mod prime(n)), A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1), A106291.

Programs

Mathematica

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}]

Formula

a(n) = A106291(prime(n)).