A356676 A certain morphism applied to A007814 that is related to the lexicographically least infinite squarefree words over the nonnegative integers.

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, 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, 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

Offset

1,4

Comments

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.

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

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.

Links

Joey Lakerdas-Gayle, Table of n, a(n) for n = 1..10000

Siddharth Berera, Andrés Gómez-Colunga, Joey Lakerdas-Gayle, John López, Mauditra Matin, Daniel Roebuck, Eric Rowland, Noam Scully, and Juliet Whidden, The lexicographically least square-free word with a given prefix, arXiv:2210.00508 [math.CO], 2022.

Joey Lakerdas-Gayle, Python code for generating prefixes of A356676

Crossrefs

Suffix of A356677. Cf. A007814, A356679.

Sequence in context: A349447 A164658 A079067 * A160271 A274912 A065134

Adjacent sequences: A356673 A356674 A356675 * A356677 A356678 A356679

Keyword

nonn

Author

Joey Lakerdas-Gayle, Aug 22 2022

Status

approved