

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
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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



