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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
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
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.)