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A106283
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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.
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1
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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
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OFFSET
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1,1
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COMMENTS
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This polynomial is the characteristic polynomial of the Fibonacci and Lucas 4-step sequences, A000078 and A073817.
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LINKS
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Table of n, a(n) for n=1..55.
Eric Weisstein's World of Mathematics, Fibonacci n-Step
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MATHEMATICA
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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]]]
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CROSSREFS
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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 A355657 A224793
Adjacent sequences: A106280 A106281 A106282 * A106284 A106285 A106286
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe, May 02 2005
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STATUS
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approved
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