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Search: id:A099243
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| A099243 |
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A variation on Flavius's sieve (A000960): Start with the primes; at the k-th sieving step, remove every p-th term of the sequence remaining after the (k-1)-st sieving step, where p is the k-th prime; iterate. |
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5
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| 2, 5, 17, 23, 47, 67, 97, 127, 137, 157, 197, 233, 283, 307, 331, 347, 419, 439, 509, 571, 599, 607, 677, 727, 761, 811, 829, 877, 937, 1009, 1093, 1129, 1187, 1229, 1297, 1303, 1367, 1427, 1447, 1523, 1663, 1697, 1753, 1787, 1879, 1901, 2027, 2087, 2113, 2131
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Index entries for sequences generated by sieves
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EXAMPLE
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Start with
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 ... and delete every second term, giving
2 5 11 17 23 31 41 47 59 67 73 83 97 103 ... and delete every 3rd term, giving
2 5 17 23 41 47 67 73 97 103 ... and delete every 5th term, giving
.... Continue for ever and what's left is the sequence.
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MAPLE
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S[1]:={seq(ithprime(i), i=1..322)}: for n from 2 to 322 do S[n]:=S[n-1] minus {seq(S[n-1][ithprime(n-1)*i], i=1..nops(S[n-1])/ithprime(n-1))} od: S[322]; - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 17 2004
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MATHEMATICA
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alle[0]=Table[Prime[i], {i, 1, 10000}]; alle[i_]:=alle[i]= Module[{zuloeschen= Table[alle[i-1][[j]], {j, Prime[i], Length[alle[i-1]], Prime[i]}]}, Complement[alle[i-1], zuloeschen]] (* alle[i] gives the sequence after the i-th iteration and here the first Prime[i] elements are fixed and will not chang in later iterations. So to get the first Prime[10]=29 terms, type *) Take[alle[10], Prime[10]] (Taktikos)
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CROSSREFS
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Cf. A000960, A099204, A000040, A099207.
Sequence in context: A069689 A106021 A032605 this_sequence A158721 A118501 A023244
Adjacent sequences: A099240 A099241 A099242 this_sequence A099244 A099245 A099246
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 16 2004
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EXTENSIONS
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More terms from Michael Taktikos (michael.taktikos(AT)hanse.net) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 16 2004
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