|
%I #9 Jul 09 2019 05:53:52
%S 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,
%T 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,
%U 1,0,2,3,0,1,2,0,1,3,0,2,1,0,2,3,0,1,2
%N Lexicographically earliest squarefree sequence of nonnegative integers whose even and odd bisections are also squarefree.
%C A sequence is squarefree if it has no subsequence of the form XX.
%C Is this sequence unbounded?
%H Rémy Sigrist, <a href="/A309013/a309013.png">Logarithmic scatterplot of the first 500000 terms of the ordinal transform of a</a>
%H Rémy Sigrist, <a href="/A309013/a309013.txt">C program for A309013</a>
%F Apparently, a(3*k+1) = 0 for any k >= 0.
%e For n = 1:
%e - "0" is squarefree,
%e - hence a(1) = 0.
%e For n = 2:
%e - "00" is not squarefree,
%e - "01" and "1" are squarefree,
%e - hence a(2) = 1.
%e For n = 3:
%e - "010" is squarefree but "00" is not,
%e - "011" is not squarefree,
%e - "012" and "02" are squarefree,
%e - hence a(3) = 2.
%e For n = 4:
%e - "0120" and "10" are squarefree,
%e - hence a(4) = 0.
%o (C) See Links section.
%Y Cf. A007814, A309011.
%K nonn
%O 1,3
%A _Rémy Sigrist_, Jul 06 2019
|
