A093343 Primes of form (prime(n)^2 + prime(n+1)^2)/2.

17, 37, 229, 2029, 14449, 22501, 25609, 28909, 32401, 42061, 57601, 72901, 116989, 176401, 181501, 265261, 304729, 324901, 378229, 462409, 497041, 695581, 804709, 1089961, 1299721, 1416109, 1664101, 1742401, 1932181, 1971241, 2712709, 2873029, 3062509, 3186229

Offset: 1

Author

Giovanni Teofilatto, Apr 26 2004

Keywords

• nonn

Comments

Except for the first term, all terms == 1 mod 6. - Zak Seidov, Dec 02 2009

Except 17, all terms == 1 mod 12. Primes of the form A028334(n+1)^2 + A024675(n)^2. - Thomas Ordowski, Jun 28 2013

Links

• Zak Seidov, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A103739.

Programs

Mathematica

Select[Mean/@Partition[Prime[Range[500]]^2,2,1],PrimeQ] (* Harvey P. Dale, Jun 16 2021 *)

Formula

Conjecture: a(n) ~ A224888(n). - Thomas Ordowski, Jul 25 2013

Extensions

Corrected and extended by Rick L. Shepherd, Nov 24 2004