cp's OEIS Frontend

A216240 Composite numbers arising in Eratosthenes sieve with removing the multiples of every other remaining numbers after 2 (see comment).

%I A216240 #29 Mar 27 2013 15:02:59
%S A216240 9,21,33,49,51,77,87,119,121,123,141,177,187,201,203,219,237,287,289,
%T A216240 291,309,319,327,329,357,393,413,417,447,451,469,471,493,501,511,517,
%U A216240 543,553,573,591,633,649,669,679,687,697,721,723,737,763,771,799,803,807
%N A216240 Composite numbers arising in Eratosthenes sieve with removing the multiples of every other remaining numbers after 2 (see comment).
%C A216240 We remove even numbers except for 2. The first two remaining numbers are 3,5. Further we remove all remaining numbers multiple of 5,except for 5. The following two remaining numbers are 7,9. Now we remove all remaining numbers multiple of 9, except for 9, etc. The sequence lists the remaining composite numbers.
%C A216240 Conjecture. There exists x_0 such that for every x>=x_0, the number of a(n)<=x is more than pi(x).
%H A216240 Peter J. C. Moses, <a href="/A216240/b216240.txt">Table of n, a(n) for n = 1..10000</a>
%t A216240 Module[{a=Insert[Range[1,1000,2], 2, 2], k=4}, While[Length[a] >= 2k, a = Flatten[{Take[a,k], Select[Take[a,-Length[a]+k], Mod[#,a[[k]]] != 0 &]}]; k+=2]; Rest[Select[a,!PrimeQ[#]&]]] (* _Peter J. C. Moses_, Mar 27 2013 *)
%Y A216240 Cf. A003309, A038179, A004280, A054103, A055398, A055399, A066680, A083140, A145592, A152021, A152114.
%K A216240 nonn
%O A216240 1,1
%A A216240 _Vladimir Shevelev_, Mar 14 2013