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 A230457 Numbers k such that there exists a Fibonacci-like sequence without multiples of k. 4
 5, 8, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is a complement of A064414. The primes in the sequence are A230359. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Brandon Avila and Tanya Khovanova, Free Fibonacci Sequences, Journal of Integer Sequences, Vol. 17 (2014), Article 14.8.5; arXiv preprint, arXiv:1403.4614 [math.NT], 2014. EXAMPLE The Lucas numbers form a Fibonacci-like sequence such that no term is divisible by 5. MATHEMATICA selQ[n_] := Do[test = Do[ If[ Divisible[ Fibonacci[k-2]*i + Fibonacci[k-1]*j, n], Return[True]], {k, 1, 2*n}]; If[test == Null, Return[False]], {i, 1, Floor[Sqrt[n]]}, {j, 1, Floor[Sqrt[n]]}]; Reap[ Do[ If[ selQ[n] =!= Null, Sow[n]], {n, 1, 100}]][[2, 1]] (* Jean-François Alcover, Oct 21 2013 *) CROSSREFS Cf. A230359, A064414. Sequence in context: A127493 A331442 A006186 * A180748 A350377 A121901 Adjacent sequences:  A230454 A230455 A230456 * A230458 A230459 A230460 KEYWORD nonn AUTHOR Brandon Avila and Tanya Khovanova, Oct 19 2013 STATUS approved

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Last modified May 21 19:42 EDT 2022. Contains 353929 sequences. (Running on oeis4.)