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%I #13 Jun 18 2017 19:46:52
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,16,18,19,20,21,22,23,25,24,26,
%T 27,29,28,30,34,31,33,32,35,36,37,38,39,41,40,42,43,45,44,46,50,47,49,
%U 48,51,53,52,54,58,55,57,56,60,68,61,59,69,62,66,63,65
%N Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms has Hamming weight <= 4.
%C Conjecturally, this is a permutation of the natural numbers.
%C This sequence has connections with A287639: here we have an upper bound, there a lower bound, on the Hamming weight of the sum of two consecutive terms.
%H Rémy Sigrist, <a href="/A288139/b288139.txt">Table of n, a(n) for n = 1..16384</a>
%H Rémy Sigrist, <a href="/A288139/a288139.gp.txt">PARI program for A288139</a>
%e The first terms, alongside a(n)+a(n+1) in binary and its Hamming weight are:
%e n a(n) a(n)+a(n+1) Hamming weight
%e -- ---- ----------- --------------
%e 1 1 11 2
%e 2 2 101 2
%e 3 3 111 3
%e 4 4 1001 2
%e 5 5 1011 3
%e 6 6 1101 3
%e 7 7 1111 4
%e 8 8 10001 2
%e 9 9 10011 3
%e 10 10 10101 3
%e 11 11 10111 4
%e 12 12 11001 3
%e 13 13 11011 4
%e 14 14 11101 4
%e 15 15 100000 1
%e 16 17 100001 2
%e 17 16 100010 2
%e 18 18 100101 3
%e 19 19 100111 4
%e 20 20 101001 3
%Y Cf. A000120, A287639.
%K nonn,look,base
%O 1,2
%A _Rémy Sigrist_, Jun 17 2017
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