A231388 Numbers n dividing the Lucas sequence u(n), defined by u(i) = 2*u(i-1) - 3*u(i-2) with initial conditions u(0)=0, u(1)=1.

1, 2, 4, 8, 16, 32, 56, 64, 112, 128, 224, 256, 272, 392, 448, 512, 544, 728, 784, 896, 992, 1024, 1088, 1456, 1568, 1792, 1904, 1984, 2048, 2176, 2408, 2744, 2912, 3136, 3584, 3808, 3968, 4096, 4352, 4624, 4816, 5096, 5488, 5824, 6176, 6272, 6944, 7168, 7616

Offset: 1

Author

Thomas M. Bridge, Nov 08 2013

Keywords

• nonn

Comments

Except for 1 and 2, all other terms are divisible by 4. This sequence contains every nonnegative power of 2.

Examples

			For n=0,...,5 we have u(n)=0,1,2,1,-4,-11. Clearly n=1,2,4 divide their respective u(n).
		

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. A088137 (Lucas sequence).

Programs

Mathematica

nn = 10000; s = LinearRecurrence[{2, -3}, {1, 2}, nn]; t = {}; Do[If[Mod[s[[n]], n] == 0, AppendTo[t, n]], {n, nn}]; t (* T. D. Noe, Nov 08 2013 *)