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

1,3

Comments

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A246079, A246699, A247197.

Sequence in context: A094786 A028871 A053705 * A049001 A049002 A247197

Adjacent sequences: A247172 A247173 A247174 * A247176 A247177 A247178

Keyword

nonn

Author

Juri-Stepan Gerasimov, Nov 30 2014

Status

approved