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A118317 a(2n-1)= smallest positive integer not occurring among the earlier terms of the sequence. a(2n) = the a(n)th positive integer among those positive integers not occurring earlier in the sequence. 4

%I #12 Jun 25 2015 04:38:44

%S 1,2,3,5,4,8,6,12,7,13,9,19,10,18,11,27,14,23,15,32,16,29,17,42,20,34,

%T 21,45,22,38,24,58,25,46,26,57,28,50,30,71,31,54,33,72,35,60,36,89,37,

%U 66,39,84,40,70,41,100,43,76,44,96,47,81,48,121,49,86,51,112,52,91,53

%N a(2n-1)= smallest positive integer not occurring among the earlier terms of the sequence. a(2n) = the a(n)th positive integer among those positive integers not occurring earlier in the sequence.

%C Sequence is a permutation of the positive integers.

%H Ivan Neretin, <a href="/A118317/b118317.txt">Table of n, a(n) for n = 1..10000</a>

%e For a(8) we want the a(4)th = 5th positive integer among those not equal to any of the first 7 terms of the sequence (those positive integers not equal to 1,2,3,5,4,8, or 6). Among those positive integers not equal to any the first 7 terms (which is the sequence 7,9,10,11,12,13...), 12 is the 5th. So a(8) = 12.

%e Now for a(9) we want the smallest positive integer that does not occur among the first 8 terms of the sequence. So a(9) = 7.

%t a = {1, 2}; Do[w = Complement[Range[Max[a] + a[[n]] + 1], a]; AppendTo[a, w[[1]]]; AppendTo[a, w[[a[[n]] + 1]]], {n, 2, 40}]; a (* _Ivan Neretin_, Jun 25 2015 *)

%Y Cf. A118315, A118316, A118318.

%K easy,nonn

%O 1,2

%A _Leroy Quet_, Apr 23 2006

%E More terms from _Joshua Zucker_, May 06 2006

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