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 A189378 #22 Feb 14 2024 17:27:48 %S A189378 6,13,19,26,34,40,47,53,61,68,74,81,89,95,102,108,116,123,129,136,142, %T A189378 150,157,163,170,178,184,191,197,205,212,218,225,233,239,246,252,259, %U A189378 267,273,280,286,294,301,307,314,322,328,335,341,349,356,362,369,375,383,390,396,403,411,417,424,430,438,445,451,458,466,472,479,485,492,500,506,513,519,527,534,540,547,555,561 %N A189378 a(n) = n + [nr/s] + [nt/s]; r=2, s=(-1+sqrt(5))/2, t=(1+sqrt(5))/2. %C A189378 Theorem: These are the numbers k such that (k+1)-sections of the Fibonacci word contain neither "000" nor "111". Proved by J. Shallit and "Walnut", Apr 06 2021. - _Don Reble_, Apr 06 2021 %H A189378 Luke Schaeffer, Jeffrey Shallit, and Stefan Zorcic, <a href="https://arxiv.org/abs/2402.08331">Beatty Sequences for a Quadratic Irrational: Decidability and Applications</a>, arXiv:2402.08331 [math.NT], 2024. See pp. 11-12. %t A189378 (See A189377.) %Y A189378 Cf. A189377, A189379. %Y A189378 Cf. A001622, A094214. %Y A189378 See also A339950. %K A189378 nonn %O A189378 1,1 %A A189378 _Clark Kimberling_, Apr 20 2011