A119474 a(2^m + k) = a(k)-th integer among those positive integers not occurring earlier in the sequence, where m >= 0, 1 <= k<= 2^m. a(1) = 1.

1, 2, 3, 5, 4, 7, 9, 12, 6, 10, 13, 16, 15, 20, 23, 27, 8, 14, 18, 22, 21, 28, 31, 35, 26, 34, 39, 43, 42, 49, 53, 58, 11, 19, 25, 32, 30, 38, 44, 48, 37, 47, 54, 59, 57, 65, 69, 74, 45, 60, 66, 72, 71, 81, 85, 90, 79, 91, 97, 102, 101, 110, 115, 121, 17, 29, 36, 46, 41, 55, 62

Offset

1,2

Comments

Sequence is a permutation of the positive integers.

Links

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

Example

8 = 2^2 +4. So since k = 4, we want the a(4)th = 5th positive integer from the sequence 6,8,10,11,12,13,..., i.e., from the sequence of positive integers not occurring among the first 7 terms of {a(k)}. So a(8) = 12.

Mathematica

a = {1}; Do[AppendTo[a, Complement[Range[Max[a] + (d = a[[i - 2^Floor[Log2[i - 1]]]])], a][[d]]], {i, 2, 71}]; a (* Ivan Neretin, May 03 2015 *)

Crossrefs

Cf. A101267, A119475.

Sequence in context: A090252 A140140 A242693 * A308098 A029654 A297769

Adjacent sequences: A119471 A119472 A119473 * A119475 A119476 A119477

Keyword

easy,nonn,look

Author

Leroy Quet, May 22 2006

Extensions

More terms from Joshua Zucker, Jul 04 2006

Status

approved