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.

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, 43, 21, 37, 24, 53, 25, 44, 26, 56, 28, 48, 29, 68, 31, 52, 32, 69, 34, 60, 35, 84, 36, 64, 39, 82, 40, 70, 41, 97, 42, 74, 45, 94, 46, 80, 47, 115, 49, 86, 50, 109, 51

Offset

1,2

Comments

Sequence is a permutation of the positive integers.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Example

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.
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.

Mathematica

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)

Crossrefs

Cf. A118316, A118317, A118318.

Sequence in context: A225040 A327173 A351412 * A280577 A075159 A362631

Adjacent sequences: A118312 A118313 A118314 * A118316 A118317 A118318

Keyword

easy,nonn

Author

Leroy Quet, Apr 23 2006

Extensions

More terms from Zak Seidov and Joshua Zucker, Apr 23 2006

Status

approved