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Search: id:A099361
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| A099361 |
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A variation on the sieve of Eratosthenes (A00040): 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 7-th prime starting with 7; and so on. |
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+0
6
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Index entries for sequences generated by sieves
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EXAMPLE
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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 for ever and the numbers not crossed off give the sequence.
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MATHEMATICA
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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)
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CROSSREFS
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Cf. A000040, A000960, A099204, A099207, A099243, A099362.
Cf. A100424
Sequence in context: A006946 A074129 A055003 this_sequence A113823 A113843 A113884
Adjacent sequences: A099358 A099359 A099360 this_sequence A099362 A099363 A099364
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 18 2004
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 18 2004
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