A309277 Sums of two primes whose difference is squarefree.

5, 7, 8, 9, 12, 15, 16, 19, 20, 21, 24, 25, 28, 32, 33, 36, 39, 40, 43, 44, 45, 48, 52, 55, 56, 60, 61, 63, 64, 68, 69, 72, 73, 75, 76, 80, 81, 84, 88, 91, 92, 96, 99, 100, 104, 105, 108, 109, 111, 112, 115, 116, 120, 124, 128, 132, 133, 136, 140, 141, 144

Offset

1,1

Links

Table of n, a(n) for n=1..61.

Example

5 is in the sequence since 5 = 2 + 3 (both prime) and 3 - 2 = 1 is squarefree.
8 is in the sequence since 8 = 5 + 3 (both prime) and 5 - 3 = 2 is squarefree.

Mathematica

Flatten[Table[If[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]) MoebiusMu[n - 2 i]^2, {i, Floor[(n - 1)/2]}] > 0, n, {}], {n, 150}]]

Crossrefs

Cf. A309152.

Sequence in context: A023726 A157724 A080644 * A180241 A047479 A080720

Adjacent sequences: A309274 A309275 A309276 * A309278 A309279 A309280

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 20 2019

Status

approved