A096063 Beginning with the sequence S(1)={1} form, in succession, the sequence S(n) for n=2,3,4,... by inserting the n smallest multiples of n that have not been used previously, in order of increasing size, n-1 of them between the final n terms of S(n-1) and the final multiple after the last term of S(n-1). {a(n)} is the limit of this process as n -> inf.

2, 3, 1, 8, 6, 12, 5, 4, 10, 16, 18, 15, 24, 9, 36, 7, 25, 14, 42, 21, 20, 32, 28, 40, 48, 64, 35, 72, 27, 30, 45, 80, 63, 49, 81, 88, 50, 90, 60, 54, 70, 99, 100, 96, 110, 11, 108, 22, 120, 33, 56, 44, 130, 55, 117, 84, 66, 144, 140, 156, 77, 168, 104, 180, 121, 192, 13

Offset

1,1

Comments

After n steps of the construction process n(n-1)/2 terms have been decided.

Links

Ivan Neretin, Table of n, a(n) for n = 1..8001

Example

1
2,1,4 (multiples of 2 placed alternately )
2,3,1,6,4,9,(multiples of 3 placed alternately )
2,3,1,8,6,12,4,16,9,20
2,3,1,8,6,12,5,4,10,16,15,9,25,20,30
The next step is to place unused multiples of 6, i.e. 18,24,36,42,48,54 at position marked ##:
2,3,1,8,6,12,5,4,10,16,##,15,##,9,##,25,##,20,##,30,##
...
After the 5th stage the terms 2,3,1,8,6,12,5,4,10,16 remain unchanged, hence form the initial 10 terms of the desired sequence.

Mathematica

mx = 13; a = {2, 1, 4}; Do[d = Complement[Range[Max[a] + 1]*n, a]; a = Join[Drop[a, -n], Riffle[Take[a, -n], Take[d, n]]], {n, 3, mx}]; Take[a, mx (mx - 1)/2] (* Ivan Neretin, Sep 06 2017 *)

Crossrefs

Sequence in context: A182223 A011152 A078298 * A101281 A106033 A121634

Adjacent sequences: A096060 A096061 A096062 * A096064 A096065 A096066

Keyword

nonn,look

Author

Amarnath Murthy, Jun 18 2004

Extensions

Extended and edited by John W. Layman, Jun 06 2005

Status

approved