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%I #13 Jul 22 2018 07:48:17
%S 2,1,3,5,10,4,8,11,6,7,18,24,14,16,42,43,12,13,15,36,9,19,20,17,23,25,
%T 21,28,22,26,33,35,37,29,40,34,27,30,50,46,31,41,54,65,70,32,76,39,81,
%U 69,45,47,48,103,53,51,49,52,56,55,57,135,121,73,59,38,58
%N Lexicographically earliest sequence of distinct positive terms such that a(1) = 2 and for any n > 0 the binary representation of a(n) appears as a substring in the binary representation of Sum_{k=1..n} a(k).
%C This sequence is a variant of A316993.
%C This sequence is conjectured to be infinite.
%C This sequence is conjectured to be a permutation of the natural numbers.
%H Rémy Sigrist, <a href="/A316994/b316994.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A316994/a316994.png">Colored scatterplot of the first 25000 terms</a> (where the color is function of the position of the binary representation of a(n) in the binary representation of Sum_{k=1..n} a(k))
%H Rémy Sigrist, <a href="/A316994/a316994.gp.txt">PARI program for A316994</a>
%e The first terms, alongside the binary representations of a(n) and of Sum_{k=1..n} a(k), are:
%e n a(n) bin(a(n)) bin(Sum_{k=1..n} a(k))
%e -- ---- --------- ----------------------
%e 1 2 10 10
%e 2 1 1 11
%e 3 3 11 110
%e 4 5 101 1011
%e 5 10 1010 10101
%e 6 4 100 11001
%e 7 8 1000 100001
%e 8 11 1011 101100
%e 9 6 110 110010
%e 10 7 111 111001
%e 11 18 10010 1001011
%e 12 24 11000 1100011
%e 13 14 1110 1110001
%e 14 16 10000 10000001
%e 15 42 101010 10101011
%e 16 43 101011 11010110
%e 17 12 1100 11100010
%e 18 13 1101 11101111
%e 19 15 1111 11111110
%e 20 36 100100 100100010
%o (PARI) See Links section.
%Y Cf. A007088, A316993.
%K nonn,base
%O 1,1
%A _Rémy Sigrist_, Jul 18 2018
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