%I #7 Oct 02 2023 13:49:11
%S 0,2,4,1,3,8,5,9,16,14,10,20,6,11,17,18,21,19,32,28,12,13,33,56,24,29,
%T 34,26,22,36,25,48,57,49,50,40,58,41,51,35,64,7,15,65,37,80,59,66,52,
%U 27,67,96,112,30,23,128,60,53,81,97,113,98,104,114,105,99
%N Lexicographically earliest infinite sequence of distinct nonnegative integers such that for any k > 0, the k-th binary digit in the even bisection is different from the k-th binary digit in the odd bisection.
%C Leading zeros in binary expansions of positive values are ignored.
%C Is this sequence a permutation of the nonnegative integers?
%H Rémy Sigrist, <a href="/A366062/a366062.gp.txt">PARI program</a>
%e The even and odd bisections, in decimal and in binary, begin as follows:
%e a(2n) |0| 4 | 3 | 5 | 16 | 10 | 6 | 17 | 21 |...
%e bin(a(2n)) |0|1 0 0|1 1|1 0 1|1 0 0 0 0|1 0 1 0|1 1 0|1 0 0 0 1|1 0 1 0 1|...
%e bin(a(2n+1)) |1 0|1|1 0 0 0|1 0 0 1|1 1 1 0|1 0 1 0 0|1 0 1 1|1 0 0 1 0|...
%e a(2n+1) | 2 |1| 8 | 9 | 14 | 20 | 11 | 18 |...
%o (PARI) See Links section.
%Y Cf. A333010.
%K nonn,base
%O 0,2
%A _Rémy Sigrist_, Sep 27 2023