A176978 Numbers n such that n^2 + 13 and n^2 + 13^2 are primes.

2, 10, 12, 28, 42, 60, 68, 108, 110, 122, 142, 180, 198, 200, 268, 282, 340, 378, 380, 418, 430, 488, 500, 502, 530, 612, 742, 788, 802, 838, 840, 912, 942, 948, 952, 1010, 1080, 1102, 1148, 1232, 1270, 1428, 1452, 1472, 1502, 1522, 1538, 1720, 1778, 1830

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 30 2010

Keywords

• nonn

Comments

Numbers are subsequence of A113536 and A176969

See comments and references of A176969

Examples

			2^2 + 13 = 17 = prime(7), 2^2 + 13^2 = 173 = prime(40), 2 is first term.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A000290, A056899, A113536, A176371, A176969.

Programs

Mathematica

Select[Range[2000],AllTrue[#^2+{13,13^2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 28 2015 *)

PARI

isok(n) = isprime(n^2 + 13) && isprime(n^2 + 13^2); \\ Michel Marcus, Aug 27 2013