This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A231958 #12 Jun 02 2025 08:49:58
%S A231958 1,2,4,8,12,16,24,32,36,48,56,64,72,96,108,112,128,132,144,156,168,
%T A231958 192,216,224,256,264,272,288,312,324,336,384,392,396,432,448,468,496,
%U A231958 504,512,528,544,552,576,624,648,672,768,784,792,816,864,896,936,972
%N 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.
%C A231958 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.
%H A231958 C. Smyth, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Smyth/smyth2.html">The Terms in Lucas Sequences Divisible by their Indices</a>, Journal of Integer Sequences, Vol.13 (2010), Article 10.2.4.
%t A231958 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 *)
%Y A231958 Cf. A000079 (powers of 2 (subsequence)).
%Y A231958 Cf. A045873 (Lucas sequence).
%K A231958 nonn,easy
%O A231958 1,2
%A A231958 _Thomas M. Bridge_, Nov 15 2013