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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.
1

%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