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A309013
Lexicographically earliest squarefree sequence of nonnegative integers whose even and odd bisections are also squarefree.
1
0, 1, 2, 0, 1, 3, 0, 1, 2, 0, 3, 1, 0, 2, 1, 0, 3, 1, 0, 4, 2, 0, 1, 2, 0, 3, 1, 0, 2, 1, 0, 3, 1, 0, 4, 3, 0, 1, 2, 0, 1, 3, 0, 2, 1, 0, 2, 3, 0, 1, 2, 0, 1, 3, 0, 4, 1, 0, 3, 1, 0, 2, 1, 0, 4, 1, 0, 3, 1, 0, 2, 3, 0, 1, 2, 0, 1, 3, 0, 2, 1, 0, 2, 3, 0, 1, 2
OFFSET
1,3
COMMENTS
A sequence is squarefree if it has no subsequence of the form XX.
Is this sequence unbounded?
FORMULA
Apparently, a(3*k+1) = 0 for any k >= 0.
EXAMPLE
For n = 1:
- "0" is squarefree,
- hence a(1) = 0.
For n = 2:
- "00" is not squarefree,
- "01" and "1" are squarefree,
- hence a(2) = 1.
For n = 3:
- "010" is squarefree but "00" is not,
- "011" is not squarefree,
- "012" and "02" are squarefree,
- hence a(3) = 2.
For n = 4:
- "0120" and "10" are squarefree,
- hence a(4) = 0.
PROG
(C) See Links section.
CROSSREFS
Sequence in context: A225682 A144185 A143987 * A112760 A096087 A128138
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jul 06 2019
STATUS
approved