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Search: id:A106284
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| A106284 |
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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. |
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+0
2
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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This polynomial is the characteristic polynomial of the Fibonacci and Lucas 5-step sequences, A001591 and A074048.
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LINKS
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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^5-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. 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: A024883 A024328 A032529 this_sequence A126145 A092729 A136186
Adjacent sequences: A106281 A106282 A106283 this_sequence A106285 A106286 A106287
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), May 02 2005
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