A201719 Primes of the form x^2 + 2y^2 such that y^2 + 2x^2 is also prime.

11, 19, 43, 59, 67, 83, 107, 139, 163, 179, 211, 251, 307, 331, 419, 443, 467, 491, 563, 571, 587, 619, 643, 811, 883, 907, 947, 971, 1019, 1091, 1123, 1171, 1259, 1291, 1307, 1427, 1531, 1571, 1579, 1667, 1699, 1747, 1787, 1811, 1907, 1979, 1987, 2003, 2011

Offset

1,1

Comments

All terms == 3 mod 8 (cf. A007520).

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Example

Corresponding pairs of primes:
(a(1),a(2))=(11,19): 11=3^2+2*1^2, 19=1^2+2*3^2
(a(3),a(4))=(43,59): 43=5^2+2*3^2, 59=3^2+2*5^2
(a(5),a(7))=(67,107): 67=7^2+2*3^2, 107=3^2+2*7^2.

Mathematica

With[{nn=50}, Take[Union[Flatten[Select[{#[[1]]^2+2#[[2]]^2, 2#[[1]]^2+ #[[2]]^2}&/@Subsets[Range[nn], {2}], And@@PrimeQ[#]&]]], nn]] (* Harvey P. Dale, Sep 15 2013 *)

Crossrefs

Cf. A154777.

Sequence in context: A260271 A275797 A294993 * A107201 A189888 A227930

Adjacent sequences: A201716 A201717 A201718 * A201720 A201721 A201722

Keyword

nonn

Author

Zak Seidov, Dec 04 2011

Status

approved