%I #6 Apr 09 2022 13:19:19
%S 0,1,2,9,4,33,18,5,8,17,66,25,36,65,10,37,16,13,34,73,132,257,50,129,
%T 72,21,130,41,20,161,74,133,32,69,26,289,68,265,146,97,264,49,514,137,
%U 100,145,258,45,144,261,42,81,260,169,82,385,40,149,322,513,148
%N Lexicographically earliest sequence of distinct nonnegative integers with alternating parity such that two consecutive terms have no common 1-bits in their binary expansions and a(2*n) = 2*a(n) for any n >= 0.
%C This sequence is a variant of A109812.
%C Terms of A004767 cannot appear in this sequence.
%H Rémy Sigrist, <a href="/A353242/a353242.txt">C++ program</a>
%F a(2^k) = 2^k for any k >= 0.
%e The first terms, alongside their binary expansions, are:
%e n a(n) bin(a(n))
%e -- ---- ---------
%e 0 0 0
%e 1 1 1
%e 2 2 10
%e 3 9 1001
%e 4 4 100
%e 5 33 100001
%e 6 18 10010
%e 7 5 101
%e 8 8 1000
%e 9 17 10001
%e 10 66 1000010
%e 11 25 11001
%e 12 36 100100
%e 13 65 1000001
%e 14 10 1010
%e 15 37 100101
%o (C++) See Links section.
%Y Cf. A109812, A004767.
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Apr 08 2022