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.

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, 21, 45, 22, 38, 24, 58, 25, 46, 26, 57, 28, 50, 30, 71, 31, 54, 33, 72, 35, 60, 36, 89, 37, 66, 39, 84, 40, 70, 41, 100, 43, 76, 44, 96, 47, 81, 48, 121, 49, 86, 51, 112, 52, 91, 53

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(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.
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.

Mathematica

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 *)

Crossrefs

Cf. A118315, A118316, A118318.

Sequence in context: A250471 A086496 A102398 * A127522 A254103 A048673

Adjacent sequences: A118314 A118315 A118316 * A118318 A118319 A118320

Keyword

easy,nonn

Author

Leroy Quet, Apr 23 2006

Extensions

More terms from Joshua Zucker, May 06 2006

Status

approved