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

1,1

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

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]]]]

Crossrefs

Cf. A099361, A100425, A100426.

Sequence in context: A215279 A082539 A168483 * A347537 A289549 A259261

Adjacent sequences: A100421 A100422 A100423 * A100425 A100426 A100427

Keyword

nonn

Author

T. D. Noe, Nov 19 2004

Status

approved