A131512 Iterated golden sieve: Iterate indefinitively the procedure giving A099267 (S2) from the natural numbers (S1) with the single difference that the rank of the deleted terms is f(n) + (p-2) to get Sp from Sp-1.

2, 3, 6, 11, 18, 27, 39, 53, 69, 81, 87, 113, 141, 171, 204, 241, 277, 304, 336, 372, 410, 432, 442, 476, 512, 543, 592, 622, 657, 700, 739, 775, 808, 855, 897, 934, 984, 1021, 1069, 1106, 1155, 1199, 1247, 1297, 1341, 1388, 1440, 1490, 1538, 1592, 1640, 1686

Offset

1,1

Links

Table of n, a(n) for n=1..52.

Example

S1 = 1,2,3,4,5,6,7,_,9,10,11,12,13,
S2 = A099267 = 2,3,5,6,8,10,11,13,14,16,18
S3: in S2 (3-2)+f(1)=3, then 5 is deleted, remaining 2,3,6,8,10,11,13,14,16,18
in this remaining sequence (3-2)+f(2)=4, then 8 is deleted, leaving 2,3,6,10,11,13,14,16,18
....
The first two terms of S2 are definitively safe. It's the same for the first three of S3, and so on;
Iterating indefinitely the procedure produces the sequence: 2,3,6,11,18,27,39,53,69,81,87,113 where the first p terms are already the first p terms of Sp and all following sequences.

Crossrefs

Cf. A099267.

Sequence in context: A377598 A157656 A059100 * A147388 A180712 A273225

Adjacent sequences: A131509 A131510 A131511 * A131513 A131514 A131515

Keyword

easy,nonn

Author

Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Aug 14 2007

Status

approved