A309011 Lexicographically earliest sequence of nonnegative integers such that for any n > 0, the palindromic word (a(n), a(n-1), ..., a(1), a(0), a(1), ..., a(n-1), a(n)) is squarefree.

0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 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, 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

Offset

0,3

Comments

A word is squarefree if it has no subsequence of the form XX.

This sequence has similarities with A007814, the lexicographically earliest squarefree sequence of nonnegative integers.

Is this sequence unbounded?

Links

Table of n, a(n) for n=0..86.

Rémy Sigrist, C program for A309011

Example

For n = 0:
- a(0) = 0.
For n = 1:
- "000" is not squarefree,
- "101" is squarefree,
- hence a(1) = 1,
For n = 2:
- "01010" is not squarefree,
- "11011" is not squarefree,
- "21012" is squarefree,
- hence a(2) = 2,
For n = 3:
- "0210120" is squarefree,
- hence a(3) = 0.

Prog

(C) See Links section.

Crossrefs

Cf. A007814.

Sequence in context: A356678 A356680 A356677 * A365921 A086713 A275730

Adjacent sequences: A309008 A309009 A309010 * A309012 A309013 A309014

Keyword

nonn

Author

Rémy Sigrist, Jul 06 2019

Status

approved