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Search: id:A106304
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| A106304 |
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Period of the Fibonacci 5-step sequence A001591 mod prime(n). |
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+0
3
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| 6, 104, 781, 2801, 16105, 30941, 88741, 13032, 12166, 70728, 190861, 1926221, 2896405, 79506, 736, 8042221, 102689, 3720, 20151120, 2863280, 546120, 39449441, 48030024, 3690720, 29509760, 104060400, 37516960, 132316201, 28231632, 6384
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This sequence is the same as the period of Lucas 5-step sequence (A106298) mod prime(n) except for n=1 and 109, which correspond to the primes 2 and 599, because 9584 is the discriminant of the characteristic polynomial x^5-x^4-x^3-x^2-x-1 and the prime factors of 9584 are 2 and 599. We have a(n) < prime(n) for the primes in A106281.
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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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n=5; Table[p=Prime[i]; a=Join[Table[ -1, {n-1}], {n}]; a=Mod[a, p]; a0=a; k=0; While[k++; s=Mod[Plus@@a, p]; a=RotateLeft[a]; a[[n]]=s; a!=a0]; k, {i, 40}]
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CROSSREFS
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Cf. A106281 (primes p such that x^5-x^4-x^3-x^2-x-1 mod p has 5 distinct zeros).
Sequence in context: A106303 A157518 A001526 this_sequence A006676 A006768 A055969
Adjacent sequences: A106301 A106302 A106303 this_sequence A106305 A106306 A106307
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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,Nov 19 2006
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