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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.
1

%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