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%I #13 Aug 09 2023 16:57:44
%S 1,2,3,5,11,7,16,9,6,18,4,13,10,15,12,23,20,8,27,19,36,26,22,17,21,31,
%T 25,14,29,28,30,57,24,32,39,43,40,34,38,46,33,35,42,37,55,44,58,48,56,
%U 52,41,45,64,63,54,61,60,49,50,51,65,47,67,88,132,73,76,68,109,59,82,87,62,98,69,70
%N Lexicographically earliest sequence of distinct positive integers such that the sum of all terms a(1)..a(n) in binary is a substring of the concatenation of all terms a(1)..a(n) in binary.
%C In the first 10000 terms the smallest number that has not yet appeared is 7026; it is conjectured all numbers eventually appear.
%C The fixed points begin 1, 2, 3, 29, 48, 68, 96, 182, 471, 839, ... . It is likely there are infinitely more.
%H Scott R. Shannon, <a href="/A364201/b364201.txt">Table of n, a(n) for n = 1..10000</a>
%e a(2) = 2 as a(1) + 2 = 1 + 2 = 3 = 11_2, which is a substring of "a(1)"_2 + "2"_2 = "1" + "10" = "110".
%e a(4) = 5 as a(1) + a(2) + a(3) + 5 = 1 + 2 + 3 + 5 = 11 = 1011_2, which is a substring "a(1)"_2 + "a(2)"_2 + "a(3)"_2 + "5"_2 = "1" + "10" + "11" + "101" = "11011101".
%e a(5) = 11 as a(1) + a(2) + a(3) + a(4) + 11 = 1 + 2 + 3 + 5 + 11 = 22 = 10110_2, which is a substring "a(1)"_2 + "a(2)"_2 + "a(3)"_2 + "a(4)"_2 + "11"_2 = "1" + "10" + "11" + "101" + "1011" = "110111011011".
%Y Cf. A363186 (base 10), A359482, A007088, A300000, A339144, A357082.
%K nonn,base
%O 1,2
%A _Scott R. Shannon_, Jul 13 2023
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