

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
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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



