A099361 A variation on the sieve of Eratosthenes (A000040): Start with the primes; the first term is 2, which is a(1) and we cross off every second prime starting with 2; the next prime not crossed off is 3, which is a(2) and we cross off every third prime starting with 3; the next prime not crossed off is 7, which is a(3) and we cross off every 7th prime starting with 7; and so on.

2, 3, 7, 13, 29, 37, 53, 79, 89, 107, 113, 139, 151, 173, 181, 223, 239, 251, 311, 317, 349, 359, 383, 397, 421, 463, 491, 503, 541, 577, 593, 613, 619, 647, 659, 683, 743, 787, 821, 857, 863, 887, 911, 983, 997, 1033, 1061, 1151, 1163, 1193, 1213, 1249

Offset

1,1

Comments

In contrast to Flavius's sieve (A000960), primes are not erased when they are crossed off; that is, primes get crossed off multiple times (see A099362).

Links

T. D. Noe, Table of n, a(n) for n=1..1000

Index entries for sequences generated by sieves

Index entries for sequences related to the Josephus Problem

Example

The first few sieving stages are as follows (X or XX indicates a prime that has been crossed off one or more times):
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 ...
2 3 X 7 XX 13 XX 19 XX 29 XX 37 XX 43 XX 53 XX 61 XX 71 XX 79 XX 89 XX ...
2 3 X 7 XX 13 XX XX XX 29 XX 37 XX XX XX 53 XX 61 XX XX XX 79 XX 89 XX ...
2 3 X 7 XX 13 XX XX XX 29 XX 37 XX XX XX 53 XX XX XX XX XX 79 XX 89 XX ...
.... Continue forever and the numbers not crossed off give the sequence.

Mathematica

nn=300; a=Prime[Range[nn]]; Do[p=a[[i]]; If[p>0, Do[a[[j]]=0, {j, i+p, nn, p}]], {i, nn}]; Rest[Union[a]] (* T. D. Noe, Nov 18 2004 *)

Crossrefs

Cf. A000040, A000960, A099204, A099207, A099243, A099362.

Cf. A100424.

Sequence in context: A233042 A055003 A175248 * A234003 A233350 A233557

Adjacent sequences: A099358 A099359 A099360 * A099362 A099363 A099364

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Nov 18 2004

Extensions

More terms from T. D. Noe and Ray Chandler, Nov 18 2004

Status

approved