A164286 Sequence resulting from an infinite series of reordering steps applied to the sequence of natural numbers A000027: At step n, when number n is at position p, the number k at position p+n is moved to position p+1.

1, 2, 4, 6, 9, 11, 15, 17, 20, 25, 27, 29, 33, 36, 40, 42, 46, 49, 51, 54, 60, 63, 65, 68, 70, 75, 77, 82, 85, 89, 92, 94, 97, 101, 103, 106, 110, 113, 115, 118, 125, 127, 132, 134, 136, 140, 143, 146, 148, 153, 157, 159, 162, 165, 169, 173, 178, 180, 182, 186, 189

Offset: 1

Author

Eric Angelini and Alois P. Heinz, Aug 12 2009

Keywords

• nice
• nonn

Comments

It seems that a(n)/n > 3 for all n > 40.

This sequence is not a permutation of the natural numbers.

Links

• Alois P. Heinz Table of n, a(n) for n = 1..5000
• Eric Angelini, Colour, drag and drop sequence
• E. Angelini, Colour, drag and drop sequence [Cached copy, with permission]

Crossrefs

Cf. A164287.

Programs

Maple

mx:= 300: # increase mx to get more items
l:= [i$i=1..3*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); l:= [l[1..p][], l[n+p], l[p+1..n+p-1][], l[n+p+1..nops(l)][]] od: for p to nops(l) do if l[p]>=mx then break fi od: a:= n-> `if`(n
				

Mathematica

max = 900; r = Range[max]; For[n = 1, True, n++, p = Position[r, n]; If[p == {} || p[[1, 1]] + n > max, Break[], c = r[[p[[1, 1]] + n]]; r = r /. {a___, n, b___, c, d___} :> {a, n, c, b, d}]]; A164286 = r[[1 ;; 61]] (* Jean-François Alcover, Jun 14 2012 *)