A309305 Sums of two primes whose difference is a nonzero square.

5, 10, 13, 18, 22, 30, 42, 46, 50, 58, 70, 78, 82, 85, 90, 98, 102, 106, 110, 114, 122, 126, 130, 138, 142, 150, 154, 158, 162, 170, 174, 178, 182, 190, 198, 202, 210, 218, 222, 229, 234, 238, 242, 246, 250, 258, 262, 270, 278, 282, 290, 294, 298, 302, 310

Offset: 1

Author

Wesley Ivan Hurt, Jul 21 2019

Keywords

• nonn

Examples

			5 is in the sequence since 5 = 2 + 3 (both prime) and 3 - 2 = 1 is a nonzero square.
10 is in the sequence since 10 = 3 + 7 (both prime) and 7 - 3 = 4 is a nonzero square.
13 is in the sequence since 13 = 2 + 11 (both prime) and 11 - 2 = 9 is a nonzero square.
18 is in the sequence since 7 + 11 (both prime) and 11 - 7 = 4 is a nonzero square.
		

Crossrefs

Cf. A000040, A000290, A309152.

Programs

Mathematica

Flatten[Table[If[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]) (Floor[Sqrt[n - 2 i]] - Floor[Sqrt[n - 2 i - 1]]), {i, Floor[(n - 1)/2]}] > 0, n, {}], {n, 300}]]