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A106291 Period of the Lucas sequence A000032 mod n. 14
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; text; internal format)
OFFSET

1,2

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.

REFERENCES

S. Vajda, Fibonacci and Lucas numbers and the Golden Section, Ellis Horwood Ltd., Chichester, 1989. See p. 89. - From N. J. A. Sloane, Feb 20 2013

LINKS

G. C. Greubel and D. Turner, Table of n, a(n) for n = 1..1200

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=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}]

CROSSREFS

Cf. A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1).

Sequence in context: A175184 A019604 A214726 * A137987 A212007 A187061

Adjacent sequences:  A106288 A106289 A106290 * A106292 A106293 A106294

KEYWORD

nonn

AUTHOR

T. D. Noe, May 02 2005

STATUS

approved

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Last modified January 22 08:58 EST 2018. Contains 298042 sequences.