A164286 -id:A164286 - cp's OEIS frontend

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

Eric Angelini and Alois P. Heinz, Aug 12 2009

This sequence is a permutation of the natural numbers.

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]

Cf. A164286.

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

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 *)

A164619 Integers of the form A164577(k)/3.

Original entry on oeis.org

4, 15, 54, 75, 132, 169, 320, 459, 735, 847, 1104, 1250, 1764, 2175, 2904, 3179, 3780, 4107, 5200, 6027, 7425, 7935, 9024, 9604, 11492, 12879, 15162, 15979, 17700, 18605, 21504, 23595, 26979, 28175, 30672, 31974, 36100, 39039, 43740, 45387, 48804

Offset: 1

Vladimir Joseph Stephan Orlovsky, Aug 17 2009

The sequence members are the third of the average of a set of smallest cubes, if integer.

			A third of the average of the first cube, A164577(1)/3=1/3, is not an integer and does not contribute to the sequence.
A third of the average of the first two cubes, A164577(2)/3=4, is an integer and defines a(1)=4 of the sequence.

Index entries for linear recurrences with constant coefficients, signature (2,-1,-1,2,-1,2,-4,2,2,-4,2,-1,2,-1,-1,2,-1).

Cf. A050248, A051456, A078617, A078618, A136116, A154293, A164286, A164576, A164577, A164578, A164579.

s=0;lst={};Do[a=(s+=(n^3)/3)/n;If[Mod[a,1]==0,AppendTo[lst,a]],{n,2*5!}]; lst
LinearRecurrence[{2,-1,-1,2,-1,2,-4,2,2,-4,2,-1,2,-1,-1,2,-1},{4,15,54,75,132,169,320,459,735,847,1104,1250,1764,2175,2904,3179,3780},50] (* Harvey P. Dale, Apr 06 2016 *)

Vec(x*(x^14 +x^13 +16*x^12 +10*x^11 +47*x^10 -22*x^9 +61*x^8 +10*x^7 +88*x^6 +8*x^5 +43*x^4 -14*x^3 +28*x^2 +7*x +4) / ((x -1)^4*(x +1)^3*(x^2 -x +1)^3*(x^2 +x +1)^2) + O(x^100)) \\ Colin Barker, Oct 27 2014

a(n) = +2*a(n-1) -a(n-2) -a(n-3) +2*a(n-4) -a(n-5) +2*a(n-6) -4*a(n-7) +2*a(n-8) +2*a(n-9) -4*a(n-10) +2*a(n-11) -a(n-12) +2*a(n-13) -a(n-14) -a(n-15) +2*a(n-16) -a(n-17). - R. J. Mathar, Jan 25 2011

G.f.: x*(x^14 +x^13 +16*x^12 +10*x^11 +47*x^10 -22*x^9 +61*x^8 +10*x^7 +88*x^6 +8*x^5 +43*x^4 -14*x^3 +28*x^2 +7*x +4) / ((x -1)^4*(x +1)^3*(x^2 -x +1)^3*(x^2 +x +1)^2). - Colin Barker, Oct 27 2014

Edited by R. J. Mathar, Aug 20 2009

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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.

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A164619 Integers of the form A164577(k)/3.

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