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 A133512 #22 Jul 09 2021 21:35:58
%S A133512 1,3,5,6,9,10,11,15,16,17,18,19,25,26,27,28,29,30,31,32,41,42,43,44,
%T A133512 45,46,47,48,49,50,51,52,53,67,68,69,70,71,72,73,74,75,76,77,78,79,80,
%U A133512 81,82,83,84,85,86,87,109,110,111,112,113,114,115,116,117,118
%N A133512 Accept F(1), reject F(1), accept F(2), reject F(2), accept F(3), ...,.
%C A133512 Start with natural numbers, then A004201 Accept one, reject one, accept two, reject two, ..., but this new analogous sequence functionally composes this with A000045 Fibonacci numbers.
%C A133512 a(n+1) is also the length of the shortest prefix of the Fibonacci word (A003849) containing some length-n block twice. - _Jeffrey Shallit_, May 15 2018
%C A133512 Complement of A344953; i.e., positions of words in A344953 that end with 0. - _Clark Kimberling_, Jun 12 2021
%H A133512 Yann Bugeaud and Dong Han Kim, <a href="https://arxiv.org/abs/1510.00282">On the b-ary expansions of log(1+1/a) and e</a>, Arxiv preprint arXiv:1510.00282 [math.NT], October 1 2015.
%H A133512 Yann Bugeaud and Dong Han Kim, <a href="https://dx.doi.org/10.2422/2036-2145.201603_002">On the b-ary expansions of log(1+1/a) and e</a>, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 17 (2017), 931-947.
%t A133512 L = {}; x = 1; Do[L = Join[L, Range[x, x + Fibonacci[n] - 1]]; x += 2 * Fibonacci[n], {n, 9}]; L (* _Giovanni Resta_, Jun 20 2016 *)
%Y A133512 Cf. A000045, A004201.
%K A133512 easy,nonn
%O A133512 1,2
%A A133512 _Jonathan Vos Post_, Nov 30 2007
%E A133512 Data corrected by _Giovanni Resta_, Jun 20 2016