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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 16:20 EST 2022. Contains 350608 sequences. (Running on oeis4.)