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

1,1

Links

Table of n, a(n) for n=1..55.

Example

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.

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}]]

Crossrefs

Cf. A000040, A000290, A309152.

Sequence in context: A313406 A313407 A313408 * A313409 A101868 A177152

Adjacent sequences: A309302 A309303 A309304 * A309306 A309307 A309308

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 21 2019

Status

approved