A231958 Numbers n dividing the Lucas sequence u(n) defined by u(i) = 2*u(i-1) - 5*u(i-2) with initial conditions u(0)=0, u(1)=1.

1, 2, 4, 8, 12, 16, 24, 32, 36, 48, 56, 64, 72, 96, 108, 112, 128, 132, 144, 156, 168, 192, 216, 224, 256, 264, 272, 288, 312, 324, 336, 384, 392, 396, 432, 448, 468, 496, 504, 512, 528, 544, 552, 576, 624, 648, 672, 768, 784, 792, 816, 864, 896, 936, 972

Offset: 1

Author

Thomas M. Bridge, Nov 15 2013

Keywords

• nonn
• easy

Comments

All terms except 1 and 2 are divisible by 4. The sequence contains every nonnegative integer power of 2. There are infinitely many multiples of 12 in the sequence.

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. A000079 (powers of 2 (subsequence)).

Cf. A045873 (Lucas sequence).

Programs

Mathematica

nn = 2000; s = LinearRecurrence[{2, -5}, {1, 2}, nn]; t = {}; Do[If[Mod[s[[n]], n] == 0, AppendTo[t, n]], {n, nn}]; t (* T. D. Noe, Nov 20 2013 *)