A099243 - OEIS

%I #23 Jun 23 2020 19:04:53

%S 2,5,17,23,47,67,97,127,137,157,197,233,283,307,331,347,419,439,509,

%T 571,599,607,677,727,761,811,829,877,937,1009,1093,1129,1187,1229,

%U 1297,1303,1367,1427,1447,1523,1663,1697,1753,1787,1879,1901,2027,2087,2113,2131

%N 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.

%H Donovan Johnson, <a href="/A099243/b099243.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>

%e Start with

%e 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

%e 2 5 11 17 23 31 41 47 59 67 73 83 97 103 ... and delete every 3rd term, giving

%e 2 5 17 23 41 47 67 73 97 103 ... and delete every 5th term, giving

%e .... Continue forever and what's left is the sequence.

%p 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_, Nov 17 2004

%t 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]] (* _Michael Taktikos_, Nov 16 2004 *)

%Y Cf. A000040, A000960, A099204, A099207.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Nov 16 2004

%E More terms from _Michael Taktikos_ and _Ray Chandler_, Nov 16 2004