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

9, 21, 33, 49, 51, 77, 87, 119, 121, 123, 141, 177, 187, 201, 203, 219, 237, 287, 289, 291, 309, 319, 327, 329, 357, 393, 413, 417, 447, 451, 469, 471, 493, 501, 511, 517, 543, 553, 573, 591, 633, 649, 669, 679, 687, 697, 721, 723, 737, 763, 771, 799, 803, 807

Offset

1,1

Comments

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.

Conjecture. There exists x_0 such that for every x>=x_0, the number of a(n)<=x is more than pi(x).

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Mathematica

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 *)

Crossrefs

Cf. A003309, A038179, A004280, A054103, A055398, A055399, A066680, A083140, A145592, A152021, A152114.

Sequence in context: A086470 A176256 A017629 * A176258 A107978 A226355

Adjacent sequences: A216237 A216238 A216239 * A216241 A216242 A216243

Keyword

nonn

Author

Vladimir Shevelev, Mar 14 2013

Status

approved