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, 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

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