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%I #12 Mar 17 2019 19:29:51
%S 1,2,3,4,5,6,7,8,9,10,12,11,13,14,15,16,17,18,20,19,21,23,24,22,25,26,
%T 28,27,29,30,31,32,33,34,36,35,37,39,40,38,41,47,45,43,49,46,42,50,44,
%U 48,51,52,56,54,57,53,55,58,60,59,61,62,63,64,65,66,68
%N Lexicographically earliest sequence of distinct positive terms such that the binary representation of the sum of two consecutive terms has at most 2 runs of ones.
%C This sequence is a variant of A306865.
%C This sequence is likely a permutation of the natural numbers.
%H Rémy Sigrist, <a href="/A306866/b306866.txt">Table of n, a(n) for n = 1..8192</a>
%H Rémy Sigrist, <a href="/A306866/a306866_1.gp.txt">PARI program for A306866</a>
%F A069010(a(n) + a(n+1)) <= 2.
%e The first terms,
%e n a(n) a(n)+a(n+1) bin(a(n)+a(n+1))
%e -- ---- ----------- ----------------
%e 1 1 3 11
%e 2 2 5 101
%e 3 3 7 111
%e 4 4 9 1001
%e 5 5 11 1011
%e 6 6 13 1101
%e 7 7 15 1111
%e 8 8 17 10001
%e 9 9 19 10011
%e 10 10 22 10110
%e 11 12 23 10111
%e 12 11 24 11000
%e 13 13 27 11011
%e 14 14 29 11101
%e 15 15 31 11111
%e 16 16 33 100001
%o (PARI) See Links section.
%Y Cf. A069010, A306865.
%K nonn,base,look
%O 1,2
%A _Rémy Sigrist_, Mar 14 2019
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