A309304 - OEIS

%I #7 Apr 20 2020 19:03:24

%S 10,13,16,18,19,20,24,25,28,30,32,36,39,40,42,43,44,48,52,55,60,61,64,

%T 68,69,72,73,78,80,81,84,88,90,91,92,96,99,100,108,112,115,120,128,

%U 132,133,138,140,144,152,156,159,162,165,168,172,180,181,184,192

%N Sums of two primes whose difference is semiprime.

%e 10 is in the sequence since 10 = 3 + 7 (both prime) and 7 - 3 = 4 is semiprime.

%e 13 is in the sequence since 13 = 2 + 11 (both prime) and 11 - 2 = 9 is semiprime.

%e 16 is in the sequence since 16 = 3 + 13 (both prime) and 13 - 3 = 10 is semiprime.

%e 18 is in the sequence since 18 = 7 + 11 (both prime) and 11 - 7 = 4 is semiprime.

%t Flatten[Table[If[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]) (KroneckerDelta[PrimeOmega[n - 2 i], 2]), {i, Floor[(n - 1)/2]}] > 0, n, {}], {n, 200}]]

%Y Cf. A309152.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Jul 21 2019