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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
0
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
1,2
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.
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 *)
CROSSREFS
Cf. A000079 (powers of 2 (subsequence)).
Cf. A045873 (Lucas sequence).
Sequence in context: A324174 A047836 A325762 * A227730 A246692 A181824
KEYWORD
nonn,easy
AUTHOR
Thomas M. Bridge, Nov 15 2013
STATUS
approved