A356676 - OEIS

%I #21 Nov 27 2022 09:02:56

%S 0,1,0,2,0,3,0,1,2,0,1,0,2,0,1,2,0,2,1,0,1,2,0,1,0,2,0,1,2,0,2,3,0,1,

%T 0,2,0,1,0,3,0,1,0,2,0,1,2,0,2,1,0,1,2,0,1,0,2,0,1,2,0,2,1,0,1,3,0,1,

%U 0,2,0,1,0,3,0,1,0,2,0,1,2,0,2,1,0,1,2,0,1,0,2,0,1,2,0,2,1,0,2,0

%N A certain morphism applied to A007814 that is related to the lexicographically least infinite squarefree words over the nonnegative integers.

%C This sequence is the result of applying the morphism alpha to the ruler sequence, A007814. The morphism alpha is defined so that alpha(0) is a particular 3226-letter word, alpha(1) is a particular 3186-letter word, and for n>=2, alpha(n) is defined recursively and has length 2*len(alpha(n-1))+2^(n+4)+10.

%C A full definition of the morphism alpha can be found in the linked Python code.

%C This is an infinite suffix of A356677. Applying the ruler morphism n->0(n+1) once results in an infinite suffix of A356679 and of the lexicographically least infinite squarefree word over the nonnegative integers beginning with k for each k>=3.

%H Joey Lakerdas-Gayle, <a href="/A356676/b356676.txt">Table of n, a(n) for n = 1..10000</a>

%H Siddharth Berera, Andrés Gómez-Colunga, Joey Lakerdas-Gayle, John López, Mauditra Matin, Daniel Roebuck, Eric Rowland, Noam Scully, and Juliet Whidden, <a href="https://arxiv.org/abs/2210.00508">The lexicographically least square-free word with a given prefix</a>, arXiv:2210.00508 [math.CO], 2022.

%H Joey Lakerdas-Gayle, <a href="/A356676/a356676.txt">Python code for generating prefixes of A356676</a>

%Y Suffix of A356677. Cf. A007814, A356679.

%K nonn

%O 1,4

%A _Joey Lakerdas-Gayle_, Aug 22 2022