A230457 Numbers k such that there exists a Fibonacci-like sequence without multiples of k.

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

Offset: 1

Author

Brandon Avila and Tanya Khovanova, Oct 19 2013

Keywords

• nonn

Comments

This sequence is a complement of A064414.

The primes in the sequence are A230359.

Examples

			The Lucas numbers form a Fibonacci-like sequence such that no term is divisible by 5.
		

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.

Crossrefs

Cf. A230359, A064414.

Programs

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 *)