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%I #8 Mar 15 2018 15:08:13
%S 1,2,5,3,8,6,4,7,9,16,11,10,12,14,15,13,36,17,19,28,18,20,26,22,21,23,
%T 24,25,31,29,68,32,30,66,33,34,61,35,37,56,39,38,51,40,41,47,42,43,44,
%U 45,48,52,46,50,49,62,27,55,54,53,57,58,141,59,60,137,63
%N Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, a(n) + a(n+1) + a(n+2) is a Fibbinary number (A003714).
%C This sequence has similarities with A266191: here we consider the sum of triples of consecutive terms, there their product.
%C This sequence is conjectured to be a permutation of the natural numbers.
%C See A300890 for a similar sequence.
%H Rémy Sigrist, <a href="/A300896/b300896.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A300896/a300896.gp.txt">PARI program for A300896</a>
%e The first terms, alongside the binary representation of triples of consecutive terms, are:
%e n a(n) binary(a(n) + a(n+1) + a(n+2))
%e -- ---- ------------------------------
%e 1 1 1000
%e 2 2 1010
%e 3 5 10000
%e 4 3 10001
%e 5 8 10010
%e 6 6 10001
%e 7 4 10100
%e 8 7 100000
%e 9 9 100100
%e 10 16 100101
%e 11 11 100001
%e 12 10 100100
%e 13 12 101001
%e 14 14 101010
%e 15 15 1000000
%e 16 13 1000010
%e 17 36 1001000
%e 18 17 1000000
%e 19 19 1000001
%e 20 28 1000010
%o (PARI) See Links section.
%Y Cf. A003714, A266191, A300890.
%K nonn,base
%O 1,2
%A _Rémy Sigrist_, Mar 14 2018