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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.
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%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