A098003 Start with positive integers. On the m-th step, shift terms a(m+1) to a(2m-1) one position to the left, then move a(m) to position (2m-1). Sequence is limit of reordering.

1, 3, 4, 2, 7, 8, 6, 11, 12, 9, 15, 16, 5, 19, 20, 14, 23, 24, 17, 27, 28, 13, 31, 32, 22, 35, 36, 25, 39, 40, 18, 43, 44, 30, 47, 48, 33, 51, 52, 10, 55, 56, 38, 59, 60, 41, 63, 64, 29, 67, 68, 46, 71, 72, 49, 75, 76, 34, 79, 80, 54, 83, 84, 57, 87, 88, 26, 91, 92

Offset

1,2

Comments

An analysis of this sequence was provided by Keith Ramsay - see link.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Keith Ramsay, Recursively Rotated Permutation. Posting in newsgroup sci.math, Sep 10 2004

Index entries for sequences that are permutations of the natural numbers

Example

[1,2,3,4,5,6,...] -> [1,3,2,4,5,6,...] -> [1,3,4,5,2,6,...] -> [1,3,4,2,6,7,...] -> [1,3,4,2,7,5,...] -> [1,3,4,2,7,8,...] -> ...

Mathematica

mx = 69; Take[Fold[Insert[Delete[#1, #2], #1[[#2]], 2 #2 - 1] &, Range[2 mx], Range[mx]], mx] (* Ivan Neretin, Mar 05 2016 *)

Crossrefs

Cf. A098046 for inverse permutation, A098486 auxiliary sequence explaning the behavior of column 1, if the sequence is written in a 3-entries-per-line table.

Sequence in context: A216221 A296431 A045901 * A026245 A266693 A026178

Adjacent sequences: A098000 A098001 A098002 * A098004 A098005 A098006

Keyword

nonn

Author

Leroy Quet, Sep 08 2004

Extensions

More terms from Hugo Pfoertner, Sep 08 2004

Status

approved