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

7, 7, 9, 15, 15, 21, 21, 27, 35, 33, 43, 45, 45, 51, 59, 65, 63, 73, 75, 75, 85, 87, 95, 105, 105, 105, 111, 111, 117, 141, 135, 143, 141, 159, 153, 163, 169, 171, 179, 185, 183, 201, 195, 201, 201, 223, 235, 231, 231, 237, 245, 243, 261, 263, 269, 275, 273

Offset: 1

Author

Zak Seidov, Jul 24 2013

Keywords

• nonn

Comments

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

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,.. .

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.

Examples

			2 + 7 = 9 = 3*3, 3 + 7 = 10 = 2*5, 5 + 9 = 14 = 2*7.
		

Crossrefs

Cf. A000040, A001358, A084704, A165138, A211280, A210497.

Programs

Maple

A224895 := proc(n)
    local p,m ;
    p := ithprime(n) ;
    for m from p+1 do
        if type(m,'odd') and numtheory[bigomega](m+p) = 2 then
            return m ;
        end if;
    end do:
end proc: # R. J. Mathar, Jul 28 2013

Mathematica

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]]
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 *)