A175600 Primes of form 4k+1 where k is a Pythagorean prime.

53, 149, 293, 389, 773, 1109, 1493, 1637, 1733, 2309, 2693, 2837, 3413, 3989, 4133, 4373, 4517, 5189, 5717, 5813, 6197, 6389, 7013, 7109, 8069, 8117, 9173, 9749, 10709, 10853, 11813, 12149, 12197, 12437, 12917, 13829, 13877, 14549, 15077, 15173

Offset: 1

Author

Zak Seidov, Jul 22 2010

Keywords

• nonn

Comments

"Double-Pythagorean" primes: primes of form 4k+1 with k prime of form 4m+1.

All terms are congruent to 5 modulo 48. - Zak Seidov, Jun 05 2014

Examples

			53 = A002144(7) = 4*13 + 1, 13 = A002144(2);
149 = A002144(16) = 4*37 + 1, 37 = A002144(5).
		

Crossrefs

Cf. A002144 (Pythagorean primes: primes of form 4n+1), A005098 (Numbers n such that 4n+1 is prime).

Programs

Mathematica

se=Select[Range[5,100000,4],PrimeQ]; (* se=A002144 *)
se2=Select[se,MemberQ[se,(#-1)/4]&]
(* (se2-1)/4 = intersection (A005098, A002144) *)