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 A231114 Numbers k dividing u(k), where the Lucas sequence is defined u(i) = u(i-1) - 4*u(i-2) with initial conditions u(0)=0, u(1)=1. 1
 1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 125, 135, 171, 225, 243, 375, 405, 435, 465, 513, 625, 675, 729, 855, 1125, 1215, 1305, 1395, 1539, 1875, 2025, 2175, 2187, 2325, 2565, 3125, 3249, 3375, 3645, 3725, 3915, 4005, 4185, 4275, 4617, 5625, 6075, 6327, 6525, 6561 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Every term (except leading term) is divisible by at least one of 3 or 5. Furthermore, this sequence contains 3^i*5^j for all i, j >= 0, that is, A003593 is a subsequence. LINKS Amiram Eldar, Table of n, a(n) for n = 1..1000 C. Smyth, The terms in Lucas sequences divisible by their indices, Journal of Integer Sequences, Vol.13 (2010), Article 10.2.4. Wikipedia, Lucas sequence EXAMPLE The sequence u(i) begins 0, 1, 1, -3, -7, 5, 33. Only for k = 1, 3, 5 does k divides u(k). MATHEMATICA nn = 10000; s = LinearRecurrence[{1, -4}, {1, 1}, nn]; t = {}; Do[If[Mod[s[[n]], n] == 0, AppendTo[t, n]], {n, nn}]; t (* T. D. Noe, Nov 06 2013 *) CROSSREFS Cf. A003593 (subsequence), A106853 (Lucas sequence). Sequence in context: A045604 A057251 A015965 * A056741 A057235 A057289 Adjacent sequences: A231111 A231112 A231113 * A231115 A231116 A231117 KEYWORD nonn AUTHOR Thomas M. Bridge, Nov 06 2013 STATUS approved

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Last modified May 27 08:54 EDT 2024. Contains 372850 sequences. (Running on oeis4.)