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

0,1

Comments

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

Links

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

Formula

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

Example

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

Prog

(PARI) 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)

Crossrefs

Cf. A000032, A152727.

Sequence in context: A127807 A122028 A340300 * A270226 A305534 A248138

Adjacent sequences: A245067 A245068 A245069 * A245071 A245072 A245073

Keyword

nonn

Author

Colin Barker, Jul 12 2014

Status

approved