

A099243


A variation on Flavius's sieve (A000960): Start with the primes; at the kth sieving step, remove every pth term of the sequence remaining after the (k1)st sieving step, where p is the kth prime; iterate.


5



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
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OFFSET

1,1


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..10000
Index entries for sequences generated by sieves
Index entries for sequences related to the Josephus Problem


EXAMPLE

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 forever and what's left is the sequence.


MAPLE

S[1]:={seq(ithprime(i), i=1..322)}: for n from 2 to 322 do S[n]:=S[n1] minus {seq(S[n1][ithprime(n1)*i], i=1..nops(S[n1])/ithprime(n1))} od: S[322]; # Emeric Deutsch, Nov 17 2004


MATHEMATICA

alle[0]=Table[Prime[i], {i, 1, 10000}]; alle[i_]:=alle[i]= Module[{zuloeschen= Table[alle[i1][[j]], {j, Prime[i], Length[alle[i1]], Prime[i]}]}, Complement[alle[i1], zuloeschen]] (* alle[i] gives the sequence after the ith 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]] (* Michael Taktikos, Nov 16 2004 *)


CROSSREFS

Cf. A000040, A000960, A099204, A099207.
Sequence in context: A307479 A106021 A032605 * A176247 A158721 A118501
Adjacent sequences: A099240 A099241 A099242 * A099244 A099245 A099246


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Nov 16 2004


EXTENSIONS

More terms from Michael Taktikos and Ray Chandler, Nov 16 2004


STATUS

approved



