A198327 Semiprimes k such that k-2 is also a semiprime.

6, 35, 51, 57, 87, 93, 95, 121, 123, 143, 145, 161, 185, 187, 203, 205, 215, 217, 219, 221, 237, 249, 267, 289, 291, 301, 303, 305, 321, 323, 329, 341, 393, 395, 413, 415, 417, 447, 453, 471, 473, 517, 519, 529, 535, 537, 545, 553, 581, 583, 591, 635, 669, 671

Offset: 1

Author

Michel Lagneau, Nov 25 2011

Keywords

• nonn

Comments

Omega(a(n)) = Omega(a(n) - Omega(a(n))) because Omega(a(n)) = 2, and a(n) - 2 is semiprime => this sequence is a subsequence of A200925.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Semiprime

Crossrefs

Cf. A001222, A092207, A200925.

Programs

Mathematica

PrimeFactorExponentsAdded[n_] := Plus @@ Flatten[Table[ #[[2]], {1}] & /@ FactorInteger[n]]; Select[ Range[ 671], PrimeFactorExponentsAdded[ # ] == PrimeFactorExponentsAdded[ # - 2] == 2 &]
SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; Select[Range[1000], SemiPrimeQ[#] && SemiPrimeQ[# - 2] &] (* T. D. Noe, Nov 27 2011 *)
#[[3,1]]&/@Select[Partition[Table[{n,PrimeOmega[n]},{n,700}],3,1], #[[1,2]]==#[[3,2]]==2&] (* Harvey P. Dale, Dec 10 2011 *)

Formula

a(n) = A092207(n) + 2.