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 A309304 Sums of two primes whose difference is semiprime. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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 * A153045 A055984 A282108 Adjacent sequences:  A309301 A309302 A309303 * A309305 A309306 A309307 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Jul 21 2019 STATUS approved

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Last modified August 9 20:09 EDT 2020. Contains 336326 sequences. (Running on oeis4.)