A309304 Sums of two primes whose difference is semiprime.

10, 13, 16, 18, 19, 20, 24, 25, 28, 30, 32, 36, 39, 40, 42, 43, 44, 48, 52, 55, 60, 61, 64, 68, 69, 72, 73, 78, 80, 81, 84, 88, 90, 91, 92, 96, 99, 100, 108, 112, 115, 120, 128, 132, 133, 138, 140, 144, 152, 156, 159, 162, 165, 168, 172, 180, 181, 184, 192

Offset: 1

Author

Wesley Ivan Hurt, Jul 21 2019

Keywords

• nonn

Examples

			10 is in the sequence since 10 = 3 + 7 (both prime) and 7 - 3 = 4 is semiprime.
13 is in the sequence since 13 = 2 + 11 (both prime) and 11 - 2 = 9 is semiprime.
16 is in the sequence since 16 = 3 + 13 (both prime) and 13 - 3 = 10 is semiprime.
18 is in the sequence since 18 = 7 + 11 (both prime) and 11 - 7 = 4 is semiprime.
		

Crossrefs

Cf. A309152.

Programs

Mathematica

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}]]