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 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. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. 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 *) CROSSREFS Cf. A000351 (powers of 5 (subsequence)). Cf. A001906 (Lucas sequence). Sequence in context: A240756 A127306 A319184 * A168145 A276407 A022310 Adjacent sequences:  A231956 A231957 A231958 * A231960 A231961 A231962 KEYWORD nonn AUTHOR Thomas M. Bridge, Nov 15 2013 STATUS approved

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Last modified January 16 19:48 EST 2022. Contains 350376 sequences. (Running on oeis4.)