A097104 Start with positive integers in order. At m-th iteration, let a(k) become a(k-1) for m+1<=k<=p_m and let a(m) become a(p_m), where p_m is the m-th prime. Record the limiting sequence.

2, 3, 4, 1, 7, 8, 10, 6, 13, 14, 16, 9, 19, 20, 22, 12, 25, 27, 29, 30, 15, 33, 35, 37, 38, 40, 18, 43, 44, 46, 21, 49, 51, 53, 54, 56, 58, 24, 61, 62, 64, 66, 28, 69, 71, 72, 31, 75, 77, 79, 80, 82, 34, 85, 87, 89, 90, 92, 94, 96, 17, 99, 101, 102, 41, 105, 107, 108, 11, 111

Offset

1,1

Comments

n-th term of limit-sequence is determined at the n-th iteration.

It is interesting to notice that 5 is moved from the fifth position to the 400th position and that the only triple is 2,3,4.

Links

Table of n, a(n) for n=1..70.

Example

{2,1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25}->
{2,3,1,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25}->
{2,3,4,5,1,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25}->
{2,3,4,1,6,7,5,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25}->
{2,3,4,1,7,5,8,9,10,11,6,12,13,14,15,16,17,18,19,20,21,22,23,24,25}->
{2,3,4,1,7,8,9,10,11,6,12,13,5,14,15,16,17,18,19,20,21,22,23,24,25}->
{2,3,4,1,7,8,10,11,6,12,13,5,14,15,16,17,9,18,19,20,21,22,23,24,25}->
{2,3,4,1,7,8,10,6,12,13,5,14,15,16,17,9,18,19,11,20,21,22,23,24,25}->...

Mathematica

lst = Table[n, {n, 100}]; f[m_] := (lst = Drop[ Insert[ lst, lst[[m]], Prime[m] + 1], {m, m}]); Do[ f[n], {n, 25}]; Take[lst, 70] (* Robert G. Wilson v, Nov 18 2004 *)

Crossrefs

Inverse is A100353. Cf. A098003, A100352.

Sequence in context: A049563 A198495 A084453 * A008310 A021431 A094936

Adjacent sequences: A097101 A097102 A097103 * A097105 A097106 A097107

Keyword

nonn

Author

Leroy Quet, Oct 24 2004

Extensions

Edited by Robert G. Wilson v, Nov 19 2004

Status

approved