This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A230457 #21 Apr 10 2021 05:53:01
%S A230457 5,8,10,11,12,13,15,16,17,18,19,20,21,22,24,25,26,28,29,30,31,32,33,
%T A230457 34,35,36,37,38,39,40,41,42,44,45,46,47,48,50,51,52,53,54,55,56,57,58,
%U A230457 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
%N A230457 Numbers k such that there exists a Fibonacci-like sequence without multiples of k.
%C A230457 This sequence is a complement of A064414.
%C A230457 The primes in the sequence are A230359.
%H A230457 Amiram Eldar, <a href="/A230457/b230457.txt">Table of n, a(n) for n = 1..10000</a>
%H A230457 Brandon Avila and Tanya Khovanova, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Avila/avila4.html">Free Fibonacci Sequences</a>, Journal of Integer Sequences, Vol. 17 (2014), Article 14.8.5; <a href="http://arxiv.org/abs/1403.4614">arXiv preprint</a>, arXiv:1403.4614 [math.NT], 2014.
%e A230457 The Lucas numbers form a Fibonacci-like sequence such that no term is divisible by 5.
%t A230457 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 *)
%Y A230457 Cf. A230359, A064414.
%K A230457 nonn
%O A230457 1,1
%A A230457 _Brandon Avila_ and _Tanya Khovanova_, Oct 19 2013