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%I #12 Dec 10 2023 09:29:37
%S 1,1,3,2,2,6,3,3,5,1,7,2,10,3,7,4,4,5,5,6,4,12,5,7,6,6,10,7,7,9,1,11,
%T 2,14,3,9,5,11,3,13,1,15,2,18,3,15,4,13,5,14,4,20,5,15,6,11,7,12,6,13,
%U 7,14,6,18,7,15,8,8,9,9,10,8,11,9,12,8,13,9,14
%N Lexicographically earliest sequence of positive integers such that the binary expansions of two consecutive terms have a 1 at the same position and for any distinct m and n, {a(m), a(m+1)} <> {a(n), a(n+1)}.
%H Rémy Sigrist, <a href="/A352836/b352836.txt">Table of n, a(n) for n = 1..9999</a>
%H Rémy Sigrist, <a href="/A352836/a352836.png">Colored scatterplot of (a(n), a(n+1)) for n < 2^18</a> (where the hue is function of n)
%H Rémy Sigrist, <a href="/A352836/a352836.txt">C++ program</a>
%e The first terms, alongside their binary expansion and {a(n), a(n+1)}, are:
%e n a(n) bin(a(n)) {a(n), a(n+1)}
%e -- ---- --------- --------------
%e 1 1 1 {1}
%e 2 1 1 {1, 3}
%e 3 3 11 {2, 3}
%e 4 2 10 {2}
%e 5 2 10 {2, 6}
%e 6 6 110 {3, 6}
%e 7 3 11 {3}
%e 8 3 11 {3, 5}
%e 9 5 101 {1, 5}
%e 10 1 1 {1, 7}
%e 11 7 111 {2, 7}
%e 12 2 10 {2, 10}
%e 13 10 1010 {3, 10}
%e 14 3 11 {3, 7}
%e 15 7 111 {4, 7}
%o (C++) See Links section.
%Y Cf. A352835.
%K nonn,look,base
%O 1,3
%A _Rémy Sigrist_, Apr 05 2022
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