A152727 -id:A152727 - cp's OEIS frontend

A245070 Smallest positive non-divisor of the n-th Lucas number (A000032).

3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2

Offset: 0

Colin Barker, Jul 12 2014

nonn

This sequence seems to be cyclic with period 12, but the equivalent sequence for the Fibonacci numbers (A152727) is not.

Lucas numbers modulo 12 are cyclic with period 24 and no 0 in the cycle (unlike Fibonacci numbers): 2, 1, 3, 4, 7, 11, 6, 5, 11, 4, 3, 7, 10, 5, 3, 8, 11, 7, 6, 1, 7, 8, 3, 11. It follows that this sequence is cyclic with period 12: 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2. - Jens Kruse Andersen, Jul 15 2014

			a(6) = 4 because lucas(6) = 18, both 2 and 3 divide 18, but 4 does not.

Jens Kruse Andersen, Table of n, a(n) for n = 0..1000

Cf. A000032, A152727.

lucas(n) = if(n==0, 2, 2*fibonacci(n-1)+fibonacci(n));
vector(1000, n, m=lucas(n-1); d=2; while(m%d==0, d++); d)

For n >= 12, a(n) = a(n-12). - Jens Kruse Andersen, Jul 15 2014

cp's OEIS Frontend

A245070 Smallest positive non-divisor of the n-th Lucas number (A000032).

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