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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.
0
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
1,2
COMMENTS
Except for 1 and 2, all other terms are divisible by 4. This sequence contains every nonnegative power of 2.
LINKS
C. Smyth, The terms in Lucas sequences divisible by their indices, Journal of Integer Sequences, Vol.13 (2010), Article 10.2.4.
EXAMPLE
For n=0,...,5 we have u(n)=0,1,2,1,-4,-11. Clearly n=1,2,4 divide their respective u(n).
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 *)
CROSSREFS
Cf. A000079 (powers of 2 (subsequence)).
Cf. A088137 (Lucas sequence).
Sequence in context: A033860 A374731 A374733 * A330012 A329824 A229614
KEYWORD
nonn
AUTHOR
Thomas M. Bridge, Nov 08 2013
STATUS
approved