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 A231404 Integers n dividing the Lucas sequence u(n), where u(i) = 2*u(i-1) - 4*u(i-2) with initial conditions u(0)=0, u(1)=1. 0
 1, 2, 3, 4, 6, 8, 9, 12, 15, 16, 18, 21, 24, 27, 30, 32, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 64, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 128, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequence consists of all nonnegative powers of 2, together with all positive multiples of 3. There are infinitely many pairs of consecutive integers in this sequence. 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,...,4 we have u(n)= 0,1,2,0,-8. Clearly n=1,2,3,4 are in the sequence. MATHEMATICA nn = 500; s = LinearRecurrence[{2, -4}, {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. A088138 (Lucas sequence). Equal to union of A008585 (multiples of 3) and A000079 (powers of 2). Sequence in context: A033501 A336504 A331827 * A316860 A097273 A006446 Adjacent sequences:  A231401 A231402 A231403 * A231405 A231406 A231407 KEYWORD nonn AUTHOR Thomas M. Bridge, Nov 08 2013 STATUS approved

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Last modified May 16 02:39 EDT 2021. Contains 343937 sequences. (Running on oeis4.)