A164287 Sequence resulting from an infinite series of reordering steps applied to the sequence of natural numbers A000027: At step n number n is moved from its position p to position p+k, where k is the actual number at position p+1.

1, 3, 2, 4, 5, 8, 6, 7, 9, 12, 13, 10, 11, 16, 14, 17, 18, 15, 20, 24, 19, 25, 21, 22, 23, 31, 26, 34, 27, 33, 28, 37, 29, 38, 36, 30, 39, 32, 35, 46, 44, 47, 40, 48, 41, 42, 43, 49, 50, 53, 45, 58, 51, 59, 61, 52, 67, 54, 68, 55, 69, 56, 70, 57, 60, 73, 62, 63, 64, 65, 66, 80

Offset: 1

Author

Eric Angelini and Alois P. Heinz, Aug 12 2009

Keywords

• nice
• nonn
• look

Comments

This sequence is a permutation of the natural numbers.

Links

• Alois P. Heinz Table of n, a(n) for n = 1..10000
• Eric Angelini, Colour, read and jump sequence
• E. Angelini, Colour, drag and drop sequence [Cached copy, with permission]
• E. Angelini, Color, read and jump sequence [Cached copy, with permission]

Crossrefs

Cf. A164286.

Programs

Maple

mx:= 620: # increase mx to get more items
l:= [i$i=1..2*mx]: pos:= proc(n) global l; local i; for i to nops(l) while l[i]<>n do od; `if`(i>nops(l), -1, i) end: for n from 1 to mx do p:= pos(n); k:= l[p+1]; l:= [l[1..p-1][], l[p+1..p+k][], l[p], l[p+k+1..nops(l)][]] od: p:= pos(mx+1): a:= n-> `if`(n
				

Mathematica

max = 200; r = Range[max]; For[n = 1, True, n++, p = Position[r, n]; If[p == {} || (q = p[[1, 1]] + r[[p[[1, 1]] + 1]] + 1) > max, Break[], c = r[[q]]; r = r /. {a___, n, b___, c, d___} :> {a, b, n, c, d}]]; A164287 = r[[1 ;; 72]] (* Jean-François Alcover, Jun 14 2012 *)