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 A304588 #20 Nov 04 2020 11:22:28 %S A304588 3,5,9,10,17,18,19,20,33,34,35,36,37,38,39,40,65,66,67,68,69,70,71,72, %T A304588 73,74,75,76,77,78,79,80,129,130,131,132,133,134,135,136,137,138,139, %U A304588 140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,257,258,259,260,261,262,263,264,265,266 %N A304588 Length of shortest prefix of the Thue-Morse word (A010060) such that some length-n block appears twice. %C A304588 lim inf a(n)/n = 5/2 and lim sup a(n)/n = 4. %C A304588 a(n) is "2-sychronized", which means that there is an automaton that accepts, in parallel, the base-2 expansions of n and a(n). For this sequence an 8-state automaton suffices. - _Jeffrey Shallit_, Mar 06 2020 %H A304588 Rémy Sigrist, <a href="/A304588/b304588.txt">Table of n, a(n) for n = 1..4096</a> %H A304588 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 A304588 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. %H A304588 Rémy Sigrist, <a href="/A304588/a304588.gp.txt">PARI program for A304588</a> %F A304588 Apparently, a(n+1) = A004756(n) + 1. - _Rémy Sigrist_, Nov 04 2020 %e A304588 For n = 3 we have a(3) = 9 because the first 9 symbols of Thue-Morse are 011010011, and 011 is the first length-3 prefix to be repeated in this prefix. %o A304588 (PARI) See Links section. %Y A304588 Cf. A010060, A004756. %K A304588 nonn %O A304588 1,1 %A A304588 _Jeffrey Shallit_, May 15 2018