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A106293 Period of the Lucas 3-step sequence A001644 mod n. 5
1, 1, 13, 4, 31, 13, 48, 8, 39, 31, 10, 52, 168, 48, 403, 16, 96, 39, 360, 124, 624, 10, 553, 104, 155, 168, 117, 48, 140, 403, 331, 32, 130, 96, 1488, 156, 469, 360, 2184, 248, 560, 624, 308, 20, 1209, 553, 46, 208, 336, 155, 1248, 168, 52, 117, 310, 48, 4680, 140 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This sequence differs from the corresponding Fibonacci sequence (A046738) at all n that are multiples of 2 or 11 because the discriminant of the characteristic polynomial x^3-x^2-x-1 is -44.

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

Eric Weisstein's World of Mathematics, Fibonacci n-Step

FORMULA

Let the prime factorization of n be p1^e1...pk^ek. Then a(n) = lcm(a(p1^e1), ..., a(pk^ek)).

MATHEMATICA

n=3; 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}]

CROSSREFS

Cf. A046738 (period of Fibonacci 3-step sequence mod n), A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1).

Sequence in context: A010219 A217426 A056139 * A046734 A226376 A222165

Adjacent sequences:  A106290 A106291 A106292 * A106294 A106295 A106296

KEYWORD

nonn

AUTHOR

T. D. Noe, May 02 2005

STATUS

approved

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Last modified October 23 22:26 EDT 2017. Contains 293833 sequences.