A120241 a(n) = (n - 2^floor(log(n)/log(2)) + 1)-th integer among those positive integers not among the earlier terms of the sequence.

1, 2, 4, 3, 6, 8, 10, 5, 9, 12, 14, 16, 18, 20, 22, 7, 13, 17, 21, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 11, 19, 25, 29, 33, 37, 41, 45, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 15, 27, 35, 43, 49, 53, 57, 61, 65

Offset: 1

Author

Leroy Quet, Jun 11 2006

Keywords

• easy
• nonn

Comments

This sequence is a permutation of the positive integers. n - 2^floor(log(n)/log(2)) + 1 = A062050(n).

Examples

			The first 6 terms of the sequence are 1,2,4,3,6,8. Now 7 - 2^floor(log(7)/log(2)) + 1 = 4. So we want the 4th term of those positive integers not occurring among the first 6 terms of the sequence (i.e., the 4th term among 5,7,9,10,11,...). So a(7) = 10.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..8191

Crossrefs

Cf. A120242, A062050.

Programs

Mathematica

Fold[Append[#1, Complement[Range[Max[#1] + #2], #1][[#2]]] &, {1},
Flatten@Table[Range[2^k], {k, 6}]] (* Ivan Neretin, Sep 24 2021 *)

Extensions

Extended by Ray Chandler, Jun 19 2006