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

1,1

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

Table of n, a(n) for n=1..60.

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

Formula

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

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}]

Crossrefs

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

Sequence in context: A212886 A127438 A303217 * A336884 A072247 A051359

Adjacent sequences: A106289 A106290 A106291 * A106293 A106294 A106295

Keyword

nonn

Author

T. D. Noe, May 02 2005

Status

approved