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Search: id:A106282
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| A106282 |
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Primes p such that the polynomial 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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5
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| 3, 5, 23, 31, 37, 59, 67, 71, 89, 97, 113, 137, 157, 179, 181, 191, 223, 229, 251, 313, 317, 331, 353, 367, 379, 383, 389, 433, 443, 449, 463, 467, 487, 509, 521, 577, 619, 631, 641, 643, 647, 653, 661, 691, 709, 719, 727, 751, 797, 823, 829, 839, 859, 881
(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 3-step sequences, A000073 and A001644.
Primes of the form 3x^2+2xy+4y^2 with x and y in Z. - T. D. Noe (noe(AT)sspectra.com), May 08 2005
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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^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. A106276 (number of distinct zeros of x^3-x^2-x-1 mod prime(n)), A106294, A106302 (period of Lucas and Fibonacci 3-step sequence mod prime(n)), A003631 (primes p such that x^2-x-1 is irreducible mod p).
Sequence in context: A136891 A106857 A106307 this_sequence A163153 A091157 A036952
Adjacent sequences: A106279 A106280 A106281 this_sequence A106283 A106284 A106285
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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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