A101267 a(1) = 1; a(n) = a(2^ceiling(log_2(n)) + 1 - n)th smallest positive integer not yet in the sequence.

1, 2, 4, 3, 7, 9, 6, 5, 13, 15, 19, 17, 11, 14, 10, 8, 24, 27, 32, 29, 37, 40, 35, 33, 21, 23, 30, 26, 18, 22, 16, 12, 44, 49, 56, 52, 62, 67, 59, 57, 73, 76, 82, 79, 69, 74, 66, 63, 39, 43, 50, 46, 58, 64, 54, 51, 34, 38, 47, 42, 28, 36, 25, 20, 84, 90, 102, 94, 110, 116, 106

Offset

1,2

Comments

Sequence is a permutation of the positive integers. 2^ceiling(log_2(n)) + 1 - n is sequence A080079 with a change of offset.

Links

Ivan Neretin, Table of n, a(n) for n = 1..8192

Example

Since 2^ceiling(log_2(n)) +1 -n = 3 at n = 6, a(6) = the a(3)th (the 4th) smallest positive integer not among the first 5 terms of the sequence. The positive integers not among the first 5 terms are 5,6,8,9,10,... The 4th of these is 9, which is a(6).

Mathematica

a[1] = 1; a[n_] := a[n] = Complement[ Range[100], Table[ a[i], {i, n - 1}]] [[ a[2^Ceiling[ Log[2, n]] + 1 - n]]]; Table[ a[n], {n, 71}] (* Robert G. Wilson v, Jan 13 2005 *)

Crossrefs

Cf. A101283, A119474.

Sequence in context: A262759 A246268 A246267 * A207633 A177877 A090568

Adjacent sequences: A101264 A101265 A101266 * A101268 A101269 A101270

Keyword

easy,nonn,look

Author

Leroy Quet, Dec 18 2004

Extensions

More terms from Robert G. Wilson v, Jan 13 2005

Status

approved