A106302 Period of the Fibonacci 3-step sequence A000073 mod prime(n).

4, 13, 31, 48, 110, 168, 96, 360, 553, 140, 331, 469, 560, 308, 46, 52, 3541, 1860, 1519, 5113, 5328, 3120, 287, 8011, 3169, 680, 51, 1272, 990, 12883, 5376, 5720, 18907, 3864, 7400, 2850, 8269, 162, 9296, 2494, 32221, 10981, 36673, 4656, 3234, 198, 5565

Offset

1,1

Comments

This sequence differs from the corresponding Lucas sequence (A106294) at n=1 and 5 because these correspond to the primes 2 and 11, which are the prime factors of -44, the discriminant of the characteristic polynomial x^3-x^2-x-1. We have a(n) < prime(n) for the primes in A106279.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = A046738(prime(n)).

Mathematica

n=3; Table[p=Prime[i]; a=Join[{1}, Table[0, {n-1}]]; 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, 60}]

Prog

(Python)
from itertools import count
from sympy import prime
def A106302(n):
    a = b = (0, )*2+(1 % (p:= prime(n)), )
    for m in count(1):
        b = b[1:] + (sum(b) % p, )
        if a == b:
            return m # Chai Wah Wu, Feb 27 2022

Crossrefs

Cf. A106273, A106279, A106294, A046738.

Sequence in context: A154753 A335981 A191189 * A158842 A100136 A097120

Adjacent sequences: A106299 A106300 A106301 * A106303 A106304 A106305

Keyword

nonn

Author

T. D. Noe, May 02 2005, Sep 18 2008

Status

approved