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 A293843 #14 Oct 19 2017 22:37:32 %S A293843 5,7,4,4,10,3,9,5,2,3,5,12,9,10,2,3,7,9,2,5,4,2,4,2,4,2,4,6,6,3,8,15, %T A293843 6,12,5,2,14,2,6,2,4,6,3,11,13,8,2,2,4,3,5,7,4,2,6,5,2,5,2,2,3,2,5,2, %U A293843 5,7,4,3,7,7,7,3,7,15,7,19,7,2,5,7,11,5,5 %N A293843 Split the infinite binary word A030302, from left to right, into the largest possible cubefree chunks; a(n) = length of n-th cubefree chunk. %C A293843 Using A030190 instead of A030302 leads to the same sequence except for the first term (that would equal 6). %C A293843 The word A030302 contains infinitely many consecutive triples of 0's (corresponding for example to the last binary digits of multiples of 8), hence A030302 has no infinite cubefree suffix, and this sequence is well defined for any n > 0. %C A293843 a(n) >= 2 for any n > 0. %C A293843 This sequence is unbounded: for any n > 0: %C A293843 - A028445(2*n) > 0, %C A293843 - hence we can choose a number in A286262, say c, with 2*n digits in binary, %C A293843 - and the subword of A030302 corresponding to c will participate in no more than two cubefree chunks, %C A293843 - and one of those chunks will have at least length n, QED. %C A293843 The first records of the sequence are (see also A293867 and A293868): %C A293843 a(n) n %C A293843 ---- -- %C A293843 5 1 %C A293843 7 2 %C A293843 10 5 %C A293843 12 12 %C A293843 15 32 %C A293843 19 76 %C A293843 21 212 %C A293843 25 412 %C A293843 35 418 %C A293843 36 2305 %C A293843 39 5118 %C A293843 47 5516 %C A293843 59 49014 %C A293843 63 104902 %C A293843 67 261530 %C A293843 71 478638 %C A293843 75 1016483 %C A293843 79 2148745 %C A293843 83 4532050 %C A293843 87 9534639 %C A293843 91 20011894 %C A293843 95 41896466 %H A293843 Rémy Sigrist, <a href="/A293843/b293843.txt">Table of n, a(n) for n = 1..10000</a> %H A293843 Rémy Sigrist, <a href="/A293843/a293843.pl.txt">PERL program for A293843</a> %e A293843 The following table shows the first terms of the sequence, alongside the corresponding cubefree chunks: %e A293843 n a(n) n-th chunk %e A293843 -- ---- ---------- %e A293843 1 5 11011 %e A293843 2 7 1001011 %e A293843 3 4 1011 %e A293843 4 4 1100 %e A293843 5 10 0100110101 %e A293843 6 3 011 %e A293843 7 9 110011011 %e A293843 8 5 11011 %e A293843 9 2 11 %e A293843 10 3 100 %Y A293843 Cf. A028445, A030190, A030302, A286262, A293867, A293868. %K A293843 nonn,base %O A293843 1,1 %A A293843 _Rémy Sigrist_, Oct 17 2017