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

1,1

Links

Table of n, a(n) for n=1..59.

Example

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.

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}]]

Crossrefs

Cf. A309152.

Sequence in context: A134651 A135548 A102502 * A345508 A153045 A055984

Adjacent sequences: A309301 A309302 A309303 * A309305 A309306 A309307

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 21 2019

Status

approved