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A357449 a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that the binary string of a(n) plus the largest previous term does not appear in the binary string concatenation of a(0)..a(n-1).

%I A357449 #12 Jan 16 2023 09:10:46
%S A357449 0,1,2,3,4,5,10,6,7,9,14,15,16,17,18,20,12,24,8,28,26,30,22,33,11,21,
%T A357449 31,32,36,37,27,35,41,13,23,40,44,38,62,46,66,19,42,63,65,69,39,59,60,
%U A357449 68,72,56,57,71,76,52,53,80,48,49,55,58,61,64,83,45,73,77,81,82,85,43,50,75,79,87,51
%N A357449 a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that the binary string of a(n) plus the largest previous term does not appear in the binary string concatenation of a(0)..a(n-1).
%C A357449 The main concentration of terms lies near the line a(n) = n; there are 26 fixed points in the first 100000 terms. The sequence is conjectured to be a permutation of the positive integers.
%H A357449 Scott R. Shannon, <a href="/A357449/a357449.png">Image for n = 0..100000</a>.
%e A357449 a(9) = 9 as the concatenation of a(0)..a(8) in binary is "0110111001011010110111" and 9 plus the largest previous term = 9 + 10 = 19 = 10011_2 which does not appear in the concatenated string. Since 10 + 8 = 18 = 10010_2 appears in the concatenated string, a(9) cannot be 8.
%o A357449 (Python)
%o A357449 from itertools import islice
%o A357449 def agen():
%o A357449     aset, astr, an, mink = {0}, "0", 0, 1
%o A357449     while True:
%o A357449         yield an; k, m = mink, max(aset)
%o A357449         while k in aset or bin(m+k)[2:] in astr: k += 1
%o A357449         while mink in aset: mink += 1
%o A357449         an = k; aset.add(an); astr += bin(an)[2:]
%o A357449 print(list(islice(agen(), 77))) # _Michael S. Branicky_, Sep 29 2022
%Y A357449 Cf. A357082, A355611, A007088, A030302, A118248, A341766.
%K A357449 nonn,base,look
%O A357449 0,3
%A A357449 _Scott R. Shannon_, Sep 29 2022