A106280 Primes p such that the polynomial x^4-x^3-x^2-x-1 mod p has 4 distinct zeros.

137, 179, 653, 859, 991, 1279, 1601, 1609, 2089, 2437, 2591, 2693, 2789, 2897, 3701, 3823, 3847, 4451, 4691, 4751, 4919, 5431, 5479, 5807, 5903, 5953, 6203, 6421, 6781, 6917, 7253, 7867, 8317, 9187, 9277, 9533, 9629, 9767, 9907, 9967, 10009, 10079

Offset

1,1

Comments

This polynomial is the characteristic polynomial of the Fibonacci and Lucas 4-step sequences, A000078 and A073817. The periods of the sequences A000078(k) mod p and A073817(k) mod p have length less than p.

Links

Table of n, a(n) for n=1..42.

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

Mathematica

t=Table[p=Prime[n]; cnt=0; Do[If[Mod[x^4-x^3-x^2-x-1, p]==0, cnt++ ], {x, 0, p-1}]; cnt, {n, 1600}]; Prime[Flatten[Position[t, 4]]]

Crossrefs

Cf. A106277 (number of distinct zeros of x^4-x^3-x^2-x-1 mod prime(n)), A106296 (period of 4-step sequence mod prime(n)).

Sequence in context: A057879 A179912 A108382 * A356980 A139510 A142651

Adjacent sequences: A106277 A106278 A106279 * A106281 A106282 A106283

Keyword

nonn

Author

T. D. Noe, May 02 2005

Status

approved