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A119474 a(2^m + k) = a(k)-th integer among those positive integers not occurring earlier in the sequence, where m >= 0, 1 <= k<= 2^m. a(1) = 1.

%I A119474 #20 Aug 27 2022 04:06:06
%S A119474 1,2,3,5,4,7,9,12,6,10,13,16,15,20,23,27,8,14,18,22,21,28,31,35,26,34,
%T A119474 39,43,42,49,53,58,11,19,25,32,30,38,44,48,37,47,54,59,57,65,69,74,45,
%U A119474 60,66,72,71,81,85,90,79,91,97,102,101,110,115,121,17,29,36,46,41,55,62
%N A119474 a(2^m + k) = a(k)-th integer among those positive integers not occurring earlier in the sequence, where m >= 0, 1 <= k<= 2^m. a(1) = 1.
%C A119474 Sequence is a permutation of the positive integers.
%H A119474 Ivan Neretin, <a href="/A119474/b119474.txt">Table of n, a(n) for n = 1..8192</a>
%e A119474 8 = 2^2 +4. So since k = 4, we want the a(4)th = 5th positive integer from the sequence 6,8,10,11,12,13,..., i.e., from the sequence of positive integers not occurring among the first 7 terms of {a(k)}. So a(8) = 12.
%t A119474 a = {1}; Do[AppendTo[a, Complement[Range[Max[a] + (d = a[[i - 2^Floor[Log2[i - 1]]]])], a][[d]]], {i, 2, 71}]; a (* _Ivan Neretin_, May 03 2015 *)
%Y A119474 Cf. A101267, A119475.
%K A119474 easy,nonn,look
%O A119474 1,2
%A A119474 _Leroy Quet_, May 22 2006
%E A119474 More terms from _Joshua Zucker_, Jul 04 2006