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A356676
A certain morphism applied to A007814 that is related to the lexicographically least infinite squarefree words over the nonnegative integers.
3
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
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.
CROSSREFS
Suffix of A356677. Cf. A007814, A356679.
Sequence in context: A349447 A164658 A079067 * A160271 A274912 A065134
KEYWORD
nonn
AUTHOR
Joey Lakerdas-Gayle, Aug 22 2022
STATUS
approved