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A106302
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Period of the Fibonacci 3-step sequence A000073 mod prime(n).
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7
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4, 13, 31, 48, 110, 168, 96, 360, 553, 140, 331, 469, 560, 308, 46, 52, 3541, 1860, 1519, 5113, 5328, 3120, 287, 8011, 3169, 680, 51, 1272, 990, 12883, 5376, 5720, 18907, 3864, 7400, 2850, 8269, 162, 9296, 2494, 32221, 10981, 36673, 4656, 3234, 198, 5565
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This sequence differs from the corresponding Lucas sequence (A106294) at n=1 and 5 because these correspond to the primes 2 and 11, which are the prime factors of -44, the discriminant of the characteristic polynomial x^3-x^2-x-1. We have a(n) < prime(n) for the primes in A106279.
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Fibonacci n-Step
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MATHEMATICA
| n=3; Table[p=Prime[i]; a=Join[{1}, Table[0, {n-1}]]; 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, 60}]
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CROSSREFS
| Cf. A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1), A106279 (primes p such that x^3-x^2-x-1 mod has 3 distinct zeros), A106294 (period of Lucas 3-step sequence mod prime(n)), A046738 (period of A000073 mod n).
Sequence in context: A042487 A154753 A191189 * A158842 A100136 A097120
Adjacent sequences: A106299 A106300 A106301 * A106303 A106304 A106305
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), May 02 2005, Sep 18 2008
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