A106293 Period of the Lucas 3-step sequence A001644 mod n.

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

Offset

1,3

Comments

This sequence can differ from the corresponding Fibonacci sequence (A046738) only when n is a multiple of 2 or 11 because the discriminant of the characteristic polynomial x^3-x^2-x-1 is -44. [Clarified by Avery Diep, Aug 22 2025]

a(n) divides A046738(n). - Avery Diep, Aug 22 2025

Links

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

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

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: A217426 A362437 A056139 * A046734 A366253 A226376

Adjacent sequences: A106290 A106291 A106292 * A106294 A106295 A106296

Keyword

nonn

Author

T. D. Noe, May 02 2005

Status

approved