

A230457


Numbers k such that there exists a Fibonaccilike 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
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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 Fibonaccilike sequence such that no term is divisible by 5.


MATHEMATICA

selQ[n_] := Do[test = Do[ If[ Divisible[ Fibonacci[k2]*i + Fibonacci[k1]*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]] (* JeanFrançois 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



