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A106284 Primes p such that the polynomial x^5-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
3, 5, 7, 11, 13, 17, 31, 37, 41, 53, 71, 79, 83, 107, 151, 157, 199, 229, 233, 239, 241, 257, 263, 277, 281, 311, 317, 331, 337, 379, 389, 409, 431, 433, 463, 467, 521, 523, 541, 547, 557, 563, 571, 577, 607, 631, 659, 677, 727, 769, 787, 809, 827, 839, 853 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This polynomial is the characteristic polynomial of the Fibonacci and Lucas 5-step sequences, A001591 and A074048.

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^5-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. A106278 (number of distinct zeros of x^5-x^4-x^3-x^2-x-1 mod prime(n)), A106298, A106304 (period of Lucas and Fibonacci 5-step sequence mod prime(n)), A003631 (primes p such that x^2-x-1 is irreducible mod p).

Sequence in context: A024328 A032529 A154866 * A126145 A206864 A155801

Adjacent sequences:  A106281 A106282 A106283 * A106285 A106286 A106287

KEYWORD

nonn

AUTHOR

T. D. Noe, May 02 2005

STATUS

approved

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Last modified May 18 22:37 EDT 2022. Contains 353826 sequences. (Running on oeis4.)