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A118315 a(1) = 1. a(2n) = smallest positive integer not occurring among the earlier terms of the sequence. a(2n+1) = the a(n)th positive integer among those positive integers not occurring earlier in the sequence. 4

%I #16 Nov 15 2021 10:42:11

%S 1,2,3,4,6,5,9,7,12,8,16,10,17,11,23,13,22,14,30,15,27,18,38,19,33,20,

%T 43,21,37,24,53,25,44,26,56,28,48,29,68,31,52,32,69,34,60,35,84,36,64,

%U 39,82,40,70,41,97,42,74,45,94,46,80,47,115,49,86,50,109,51

%N a(1) = 1. a(2n) = smallest positive integer not occurring among the earlier terms of the sequence. a(2n+1) = 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="/A118315/b118315.txt">Table of n, a(n) for n = 1..10000</a>

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

%e Now for a(10) we want the smallest positive integer that does not occur among the first 9 terms of the sequence. So a(10) = 8.

%t s={1};a=Range[1000];b=Rest[a];Do[ c=If[OddQ[n],b[[s[[(n-1)/2]]]],b[[1]]];b=Complement[b,{c}];AppendTo[s,c],{n,2,200}];s (Seidov)

%Y Cf. A118316, A118317, A118318.

%K easy,nonn

%O 1,2

%A _Leroy Quet_, Apr 23 2006

%E More terms from _Zak Seidov_ and _Joshua Zucker_, Apr 23 2006

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Last modified March 28 13:19 EDT 2024. Contains 371254 sequences. (Running on oeis4.)