

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.


6



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
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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


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



