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A224895 Let p = prime(n). Smallest odd number m > p such that m + p is semiprime.

%I A224895 #24 Nov 07 2023 08:17:45
%S A224895 7,7,9,15,15,21,21,27,35,33,43,45,45,51,59,65,63,73,75,75,85,87,95,
%T A224895 105,105,105,111,111,117,141,135,143,141,159,153,163,169,171,179,185,
%U A224895 183,201,195,201,201,223,235,231,231,237,245,243,261,263,269,275,273
%N A224895 Let p = prime(n). Smallest odd number m > p such that m + p is semiprime.
%C A224895 Apparently a(n) = A210497(n) for n>1, which basically indicates that the search for the smallest even semiprime larger than 2*prime(n) produces 2*prime(n+1). - _R. J. Mathar_, Jul 27 2013
%C A224895 a(n) <= A165138(n); a(n) = A165138(n) when a(n) is prime, corresponding n's: 1, 2, 11, 15, 18, 36, 39, 46, 54, 55, 58, 73, 91,.. .
%C A224895 Also of interest is that sequence in not monotonic: e.g., a(10) - a(9) = 33 - 35 = -2, a(31) - a(30) = 135 - 141 = -6.
%e A224895 2 + 7 = 9 = 3*3, 3 + 7 = 10 = 2*5, 5 + 9 = 14 = 2*7.
%p A224895 A224895 := proc(n)
%p A224895     local p,m ;
%p A224895     p := ithprime(n) ;
%p A224895     for m from p+1 do
%p A224895         if type(m,'odd') and numtheory[bigomega](m+p) = 2 then
%p A224895             return m ;
%p A224895         end if;
%p A224895     end do:
%p A224895 end proc: # _R. J. Mathar_, Jul 28 2013
%t A224895 Reap[Sow[7];Do[p=Prime[n];k=p+2;While[!PrimeQ[r=(p+k)/2],k=k+2];Sow[k],{n,2,100}]][[2,1]]
%t A224895 son[n_]:=Module[{m=If[EvenQ[n],n+1,n+2]},While[PrimeOmega[n+m]!=2,m = m+2]; m]; Table[son[n],{n,Prime[Range[60]]}] (* _Harvey P. Dale_, Apr 24 2017 *)
%Y A224895 Cf. A000040, A001358, A084704, A165138, A211280, A210497.
%K A224895 nonn
%O A224895 1,1
%A A224895 _Zak Seidov_, Jul 24 2013