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A106293 Period of the Lucas 3-step sequence A001644 mod n. 5


%S 1,1,13,4,31,13,48,8,39,31,10,52,168,48,403,16,96,39,360,124,624,10,

%T 553,104,155,168,117,48,140,403,331,32,130,96,1488,156,469,360,2184,

%U 248,560,624,308,20,1209,553,46,208,336,155,1248,168,52,117,310,48,4680,140

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

%C 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.

%H T. D. Noe, <a href="/A106293/b106293.txt">Table of n, a(n) for n=1..1000</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=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}]

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

%K nonn

%O 1,3

%A _T. D. Noe_, May 02 2005

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Last modified April 21 07:26 EDT 2021. Contains 343146 sequences. (Running on oeis4.)