A100424 A sieve transform applied three times to the positive integers.

2, 3, 13, 37, 107, 139, 223, 251, 359, 397, 503, 647, 683, 857, 887, 1033, 1151, 1249, 1291, 1429, 1493, 1601, 1667, 1783, 1831, 2003, 2053, 2267, 2377, 2459, 2593, 2677, 2753, 2801, 2903, 3119, 3209, 3347, 3461, 3557, 3607, 3727, 3851, 4079, 4139, 4243

Offset: 1

Author

T. D. Noe, Nov 19 2004

Keywords

• nonn

Comments

The process is described in A099361. The first application of the sieve transform produces the prime numbers A000040. The second application yields sequence A099361. In principle, the sieve transform can be applied to any sequence of positive integers. For instance, the sieve transform of the positive even numbers is 2, 4, 8, 16,.... Also note that the transform can produce a finite sequence. See A100425 and A100426 for more examples.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A099361, A100425, A100426.

Programs

Mathematica

SieveTransform[b_List] := Module[{d, nn=Length[b], a=b}, Do[d=a[[i]]; If[d>1, Do[a[[j]]=-1, {j, i+d, nn, d}]], {i, nn}]; DeleteCases[a, -1]]; SieveTransform[SieveTransform[SieveTransform[Range[2, 5000]]]]