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A106291 Period of the Lucas sequence A000032 mod n. 14


%S 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,

%T 84,72,48,14,24,30,48,40,36,16,24,76,18,56,12,40,48,88,30,24,48,32,24,

%U 112,60,72,84,108,72,20,48,72,42,58,24,60,30,48,96,28,120,136,36,48,48

%N Period of the Lucas sequence A000032 mod n.

%C 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.

%D 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

%H G. C. Greubel and D. Turner, <a href="/A106291/b106291.txt">Table of n, a(n) for n = 1..1200</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step</a>

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

%t 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}]

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

%K nonn

%O 1,2

%A _T. D. Noe_, May 02 2005

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Last modified February 17 17:27 EST 2018. Contains 299296 sequences. (Running on oeis4.)