A231959 Numbers n dividing the Lucas sequence u(n) defined by u(i) = 3*u(i-1) - u(i-2) with initial conditions u(0)=0, u(1)=1.

1, 5, 6, 12, 18, 24, 25, 30, 36, 48, 54, 55, 60, 72, 84, 90, 96, 108, 120, 125, 144, 150, 162, 168, 180, 192, 216, 240, 252, 270, 275, 276, 288, 300, 306, 324, 330, 336, 342, 360, 384, 420, 432, 450, 480, 486, 504, 540, 552, 576, 588, 600, 605, 612, 625

Offset: 1

Author

Thomas M. Bridge, Nov 15 2013

Keywords

• nonn

Comments

All terms except 1 are divisible by either 5 or 6. The sequence contains every nonnegative integer power of 5. There are infinitely many multiples of 6 in the sequence and infinitely many consecutive integers in the sequence (for example, 5,6 or 24,25, or 54,55).

Links

• C. Smyth, The Terms in Lucas Sequences Divisible by their Indices, Journal of Integer Sequences, Vol.13 (2010), Article 10.2.4.

Crossrefs

Cf. A000351 (powers of 5 (subsequence)).

Cf. A001906 (Lucas sequence).

Programs

Mathematica

nn = 1000; s = LinearRecurrence[{3, -1}, {1, 3}, nn]; t = {}; Do[If[Mod[s[[n]], n] == 0, AppendTo[t, n]], {n, nn}]; t (* T. D. Noe, Nov 22 2013 *)