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

1,1

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