%I #28 May 10 2021 03:53:11

%S 6,35,51,57,87,93,95,121,123,143,145,161,185,187,203,205,215,217,219,

%T 221,237,249,267,289,291,301,303,305,321,323,329,341,393,395,413,415,

%U 417,447,453,471,473,517,519,529,535,537,545,553,581,583,591,635,669,671

%N Semiprimes k such that k-2 is also a semiprime.

%C 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.

%H Harvey P. Dale, <a href="/A198327/b198327.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime</a>

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

%t PrimeFactorExponentsAdded[n_] := Plus @@ Flatten[Table[ #[[2]], {1}] & /@ FactorInteger[n]]; Select[ Range[ 671], PrimeFactorExponentsAdded[ # ] == PrimeFactorExponentsAdded[ # - 2] == 2 &]

%t 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 *)

%t #[[3,1]]&/@Select[Partition[Table[{n,PrimeOmega[n]},{n,700}],3,1], #[[1,2]]==#[[3,2]]==2&] (* _Harvey P. Dale_, Dec 10 2011 *)

%Y Cf. A001222, A092207, A200925.

%K nonn

%O 1,1

%A _Michel Lagneau_, Nov 25 2011