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%I #11 Jun 09 2016 21:48:36
%S 1,2,4,6,9,11,15,17,20,25,27,29,33,36,40,42,46,49,51,54,60,63,65,68,
%T 70,75,77,82,85,89,92,94,97,101,103,106,110,113,115,118,125,127,132,
%U 134,136,140,143,146,148,153,157,159,162,165,169,173,178,180,182,186,189
%N 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.
%C It seems that a(n)/n > 3 for all n > 40.
%C This sequence is not a permutation of the natural numbers.
%H Alois P. Heinz <a href="/A164286/b164286.txt">Table of n, a(n) for n = 1..5000</a>
%H Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/ColourDragDrop.htm">Colour, drag and drop sequence</a>
%H E. Angelini, <a href="/A164286/a164286.pdf">Colour, drag and drop sequence</a> [Cached copy, with permission]
%p mx:= 300: # increase mx to get more items
%p 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<p, l[n], NULL): seq(a(n), n=1..p);
%t 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 *)
%Y Cf. A164287.
%K nice,nonn
%O 1,2
%A _Eric Angelini_ and _Alois P. Heinz_, Aug 12 2009
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