A247175 Numbers n such that 2*(n^2 + 2) - 1 and 2*(n^2 + 2) + 1 are both prime.

0, 1, 2, 7, 23, 47, 98, 208, 268, 278, 352, 422, 712, 803, 833, 887, 1022, 1048, 1052, 1057, 1297, 1372, 1517, 1603, 1657, 1717, 1748, 1888, 1988, 2102, 2207, 2233, 2357, 2548, 2567, 2753, 2828, 2893, 2938, 3017, 3362, 3367, 3572, 3817, 3908, 4247, 4268, 4312, 4403, 4408, 4412, 4478

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 30 2014

Keywords

• nonn

Comments

Numbers n such that 2*n^2 + 3 and 2*n^2 + 5 are both prime.

Examples

			2 is in this sequence because 2*2^2 + 3 = 11 and 2*2^2 + 5 = 13 are both prime.
		

Links

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

Crossrefs

Cf. A246079, A246699, A247197.

Programs

Magma

[ n: n in [0..4500] | IsPrime(2*(n^2+2)-1) and IsPrime(2*(n^2+2)+1) ];

Mathematica

a247175[n_Integer] := Select[Range[n], And[PrimeQ[2*(#^2 + 2) - 1], PrimeQ[2*(#^2 + 2) + 1]] &]; a247175[4500] (* Michael De Vlieger, Nov 30 2014 *)
Select[Range[0,4500],AllTrue[2#^2+{3,5},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 09 2019 *)