A099361 - OEIS

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

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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

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