A228440 Numbers n dividing u(n), where the Lucas sequence is defined u(i) = u(i-1) - 3*u(i-2) with initial conditions u(0)=0, u(1)=1.

1, 11, 121, 253, 1331, 2783, 5819, 11891, 14641, 29161, 30613, 64009, 130801, 133837, 161051, 273493, 320771, 336743, 558877, 640343, 670703, 704099, 895873, 1438811, 1472207, 1771561, 3008423, 3078251, 3528481, 3544453, 3704173, 6147647, 6290339, 7027801

Offset: 1

Author

Thomas M. Bridge, Nov 02 2013

Keywords

• nonn

Comments

Since the absolute value of the discriminant of the characteristic polynomial is prime (=11), the sequence contains every nonnegative integer power of 11 (A001020 is subsequence). Other terms are formed on multiplication of 11^k by sporadic primes.

Examples

			u(1)=1 and u(11)=253. Clearly n divides u(n) for these terms.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 1..65
• 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. A214733 (Lucas sequence u(n) ignoring sign).

Cf. A001020 (powers of 11).

Programs

Mathematica

nn = 10000; s = LinearRecurrence[{1, -3}, {1, 1}, nn]; t = {}; Do[
If[Mod[s[[n]], n] == 0, AppendTo[t, n]], {n, nn}]; t (* T. D. Noe, Nov 06 2013 *)

Extensions

a(27)-a(34) from Lars Blomberg, Feb 15 2016