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

Author

Thomas M. Bridge, Nov 06 2013

Keywords

• nonn

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.

Examples

			The sequence u(i) begins 0, 1, 1, -3, -7, 5, 33. Only for k = 1, 3, 5 does k divides u(k).
		

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

Crossrefs

Cf. A003593 (subsequence), A106853 (Lucas sequence).

Programs

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 *)