cp's OEIS Frontend

A357433 a(1) = 1; a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier such that the binary string of a(n) plus the sum of all previous terms appears in the binary string concatenation of a(1)..a(n-1).

%I A357433 #11 Jan 16 2023 09:10:46
%S A357433 1,2,3,5,12,4,9,10,11,16,14,6,7,18,17,13,15,8,20,22,24,33,26,31,21,19,
%T A357433 25,35,30,28,56,34,36,43,32,42,37,23,29,38,27,58,45,60,46,52,44,50,72,
%U A357433 53,54,41,65,47,40,48,66,51,64,49,57,61,67,93,77,59,74,100,75,69,91,73,83,71,81,39,82
%N A357433 a(1) = 1; a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier such that the binary string of a(n) plus the sum of all previous terms appears in the binary string concatenation of a(1)..a(n-1).
%C A357433 The sequence is conjectured to be a permutation of the positive integers. In the first 20000 terms there are twenty-five fixed points starting 3, 37, 84, 99, 103, 166.
%H A357433 Scott R. Shannon, <a href="/A357433/a357433.png">Image of the first 20000 terms</a>. The green line is a(n) = n.
%e A357433 a(5) = 12 as a(1) + a(2) + a(3) + a(4) + 12 = 1 + 2 + 3 + 5 + 12 = 23 = 10111_2, and "10111" appears in the string concatenation of the binary values of a(1)..a(4) = "11011101".
%Y A357433 Cf. A357432 (base 10), A000027, A007088, A007908, A000217, A341766, A337227.
%K A357433 nonn,base
%O A357433 1,2
%A A357433 _Scott R. Shannon_, Sep 28 2022