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A106291
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Period of the Lucas sequence A000032 mod n.
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1
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1, 3, 8, 6, 4, 24, 16, 12, 24, 12, 10, 24, 28, 48, 8, 24, 36, 24, 18, 12, 16, 30, 48, 24, 20, 84, 72, 48, 14, 24, 30, 48, 40, 36, 16, 24, 76, 18, 56, 12, 40, 48, 88, 30, 24, 48, 32, 24, 112, 60, 72, 84, 108, 72, 20, 48, 72, 42, 58, 24, 60, 30, 48, 96, 28, 120, 136, 36, 48, 48
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This sequence differs from the Fibonacci periods (A001175) only when n is a multiple of 5, which can be traced to 5 being the discriminant of the characteristic polynomial x^2-x-1.
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LINKS
| Eric Weisstein's World of Mathematics, Fibonacci n-Step
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FORMULA
| Let the prime factorization of n be p1^e1...pk^ek. Then a(n) = lcm(a(p1^e1), ..., a(pk^ek)).
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MATHEMATICA
| n=2; Table[p=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, 70}]
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CROSSREFS
| Cf. A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1).
Sequence in context: A016627 A175184 A019604 * A137987 A187061 A020809
Adjacent sequences: A106288 A106289 A106290 * A106292 A106293 A106294
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), May 02 2005
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