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A106295
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Period of the Lucas 4-step sequence A073817 mod n.
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5
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1, 5, 26, 10, 312, 130, 342, 20, 78, 1560, 120, 130, 84, 1710, 312, 40, 4912, 390, 6858, 1560, 4446, 120, 12166, 260, 1560, 420, 234, 1710, 280, 1560, 61568, 80, 1560, 24560, 17784, 390, 1368, 34290, 1092, 1560, 240, 22230, 162800, 120, 312, 60830, 103822
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OFFSET
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1,2
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COMMENTS
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This sequence is the same as the period of Fibonacci 4-step sequence (A000078) mod n for n<563 because the discriminant of the characteristic polynomial x^4-x^3-x^2-x-1 is -563. The two sequences differ only at n that are multiples of 563.
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LINKS
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Table of n, a(n) for n=1..47.
Eric Weisstein's World of Mathematics, Fibonacci n-Step
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FORMULA
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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
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n=4; 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, 60}]
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CROSSREFS
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Cf. A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1).
Sequence in context: A137113 A137115 A060063 * A057688 A259207 A300005
Adjacent sequences: A106292 A106293 A106294 * A106296 A106297 A106298
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe, May 02 2005
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STATUS
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approved
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