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 A345717 #16 Oct 24 2024 15:09:16 %S A345717 4,6,7,11,13,17,18,20,24,26,27,30,31,33,37,38,40,41,42,43,44,48,50,51, %T A345717 55,57,61,62,63,64,68,70,74,75,77,79,81,85,86,87,88,92,94,95,98,99, %U A345717 101,105,107,108,111,112,114,116,118,119,122,123,125,129,131,132 %N A345717 Orders of abelian cubes in the tribonacci word A080843. %C A345717 An abelian cube is a word of the form x x' x'', where x' and x'' are permutations of x, like the English word "deeded". The order of an abelian cube is the length of x. %H A345717 Pierre Popoli, Jeffrey Shallit, and Manon Stipulanti, <a href="https://arxiv.org/abs/2410.02409">Additive word complexity and Walnut</a>, arXiv:2410.02409 [math.CO], 2024. See p. 17. %F A345717 There is a deterministic finite automaton of 1169 states that takes n in its tribonacci representation as input and accepts if and only if there is an abelian cube of order n. It can be obtained with the Walnut theorem-prover. %e A345717 Here are the earliest-appearing abelian cubes of the first few orders: %e A345717 n = 4: 2010.0102.0102 %e A345717 n = 6: 102010.010201.010201 %e A345717 n = 7: 0102010.0102010.1020100 %e A345717 n = 11: 02010010201.01020100102.01020100102 %Y A345717 Cf. A080843. %K A345717 nonn %O A345717 1,1 %A A345717 _Jeffrey Shallit_, Jun 24 2021