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A106283 Primes p such that the polynomial x^4-x^3-x^2-x-1 mod p has no zeros; i.e., the polynomial is irreducible over the integers mod p. 1
2, 5, 11, 13, 31, 43, 53, 79, 83, 89, 97, 103, 109, 131, 139, 151, 197, 199, 229, 233, 239, 251, 257, 271, 283, 313, 317, 347, 359, 367, 379, 389, 433, 443, 461, 479, 487, 521, 569, 571, 577, 593, 599, 601, 617, 631, 641, 643, 647, 659, 673, 677, 719, 769, 797 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This polynomial is the characteristic polynomial of the Fibonacci and Lucas 4-step sequences, A000078 and A073817.

LINKS

Table of n, a(n) for n=1..55.

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

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, 200}]; Prime[Flatten[Position[t, 0]]]

CROSSREFS

Cf. A106277 (number of distinct zeros of x^4-x^3-x^2-x-1 mod prime(n)), A106296 (period of Lucas 4-step sequence mod prime(n)), A003631 (primes p such that x^2-x-1 is irreducible in mod p).

Sequence in context: A215214 A221868 A220141 * A020629 A224793 A272852

Adjacent sequences:  A106280 A106281 A106282 * A106284 A106285 A106286

KEYWORD

nonn

AUTHOR

T. D. Noe, May 02 2005

STATUS

approved

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Last modified April 9 12:51 EDT 2020. Contains 333352 sequences. (Running on oeis4.)