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Search: id:A106281
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| A106281 |
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Primes p such that the polynomial x^5-x^4-x^3-x^2-x-1 mod p has 5 distinct zeros. |
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+0
4
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| 691, 733, 3163, 4259, 4397, 5419, 6637, 6733, 8009, 8311, 9803, 11731, 14923, 17291, 20627, 20873, 22777, 25111, 26339, 27947, 29339, 29389, 29527, 29917, 34123, 34421, 34739, 34757, 36527, 36809, 38783, 40433, 40531, 41131, 42859, 43049
(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. The periods of the sequences A001591(k) mod p and A074048(k) mod p have length less than p.
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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, 5000}]; Prime[Flatten[Position[t, 5]]]
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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 mod prime(n)).
Adjacent sequences: A106278 A106279 A106280 this_sequence A106282 A106283 A106284
Sequence in context: A001067 A046988 A029825 this_sequence A127341 A135316 A046753
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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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