A309013 Lexicographically earliest squarefree sequence of nonnegative integers whose even and odd bisections are also squarefree.

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?

Links

Table of n, a(n) for n=1..87.

Rémy Sigrist, Logarithmic scatterplot of the first 500000 terms of the ordinal transform of a

Rémy Sigrist, C program for A309013

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

Cf. A007814, A309011.

Sequence in context: A225682 A144185 A143987 * A112760 A096087 A128138

Adjacent sequences: A309010 A309011 A309012 * A309014 A309015 A309016

Keyword

nonn

Author

Rémy Sigrist, Jul 06 2019

Status

approved