A231290 Numbers k dividing u(k), where the Lucas sequence is defined u(i) = u(i-1) - 5*u(i-2) with initial conditions u(0)=0, u(1)=1.

1, 12, 19, 24, 36, 48, 72, 84, 96, 108, 144, 168, 192, 216, 228, 252, 288, 324, 336, 361, 384, 432, 456, 504, 576, 588, 648, 672, 684, 744, 756, 768, 816, 864, 912, 972, 1008, 1092, 1152, 1176, 1296, 1344, 1368, 1488, 1512, 1536, 1596, 1632, 1728, 1764

Offset: 0

Author

Thomas M. Bridge, Nov 06 2013

Keywords

• nonn

Comments

Contains every nonnegative power of 19. All terms that are not a power of 19 are multiples of 12.

Links

• C. Smyth, The terms in Lucas sequences divisible by their indices, Journal of Integer Sequences, Vol.13 (2010), Article 10.2.4.

Crossrefs

Cf. A001029 (powers of 19 (subsequence)).

Programs

Mathematica

nn = 3000; s = LinearRecurrence[{1, -5}, {1, 1}, nn]; t = {}; Do[If[Mod[s[[n]], n] == 0, AppendTo[t, n]], {n, nn}]; t (* T. D. Noe, Nov 08 2013 *)