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

Author

N. J. A. Sloane, Nov 18 2004

Keywords

• nonn
• easy
• nice

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).

Examples

			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.
		

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

Crossrefs

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

Cf. A100424.

Programs

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 *)

Extensions

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