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A106297 Period of the Lucas 5-step sequence A074048 mod n. 3
1, 1, 104, 6, 781, 104, 2801, 12, 312, 781, 16105, 312, 30941, 2801, 81224, 24, 88741, 312, 13032, 4686, 291304, 16105, 12166, 312, 3905, 30941, 936, 16806, 70728, 81224, 190861, 48, 1674920, 88741, 2187581, 312, 1926221, 13032, 3217864, 9372, 2896405 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This sequence differs from the corresponding Fibonacci sequence (A106303) at all n that are multiples of 2 or 599 because 9584 is the discriminant of the characteristic polynomial x^5-x^4-x^3-x^2-x-1 and the prime factors of 9584 are 2 and 599.

LINKS

Table of n, a(n) for n=1..41.

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=5; 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, 50}]

CROSSREFS

Cf. A106303 (period of Fibonacci 5-step sequence mod n), A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1).

Sequence in context: A088584 A238490 A097014 * A090849 A091025 A054904

Adjacent sequences:  A106294 A106295 A106296 * A106298 A106299 A106300

KEYWORD

nonn

AUTHOR

T. D. Noe, May 02 2005, Nov 19 2006

STATUS

approved

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Last modified October 20 20:04 EDT 2019. Contains 328270 sequences. (Running on oeis4.)