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

Author

Leroy Quet, Dec 18 2004

Keywords

• easy
• nonn
• look

Comments

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

Examples

			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).
		

Links

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

Crossrefs

Cf. A101283, A119474.

Programs

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 *)

Extensions

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