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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.
2
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?
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
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jul 06 2019
STATUS
approved