A174362 Odd primes such that 2*p^2-+39 are also prime.

5, 7, 19, 23, 37, 89, 107, 131, 239, 251, 257, 271, 397, 433, 439, 449, 547, 673, 1009, 1049, 1297, 1373, 1427, 1451, 1471, 1609, 1709, 2003, 2053, 2311, 2351, 2357, 2417, 2731, 2749, 2791, 3313, 3457, 4159, 4283, 4289, 4447, 4451, 4783, 5227, 5651, 5683

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

For p = 5, 2*5^2 - 39 = 11 and 2(5^2) + 39 = 89, both 11 and 89 are prime, thus 5 is in the sequence.
For p = 7, 2*7^2 -  39 = 59 and 2(7^2) + 39 = 137, both 59 and 137 are prime, thus 7 is in the sequence.
11 is NOT in the sequence, because even though 2(11^2) + 39 does give a prime (281), 2(11^2) - 39 does not, giving 203 = 7 * 29.

Mathematica

Select[Prime[Range[3, 1000]], PrimeQ[2#^2 - 39] && PrimeQ[2#^2 + 39] &] (* Vincenzo Librandi, Oct 14 2012 *)

Prog

(Magma) [p: p in PrimesInInterval(3, 6000) | IsPrime(2*p^2-39) and IsPrime(2*p^2+39)];

Crossrefs

Sequence in context: A046078 A075409 A258655 * A268608 A058079 A076787

Adjacent sequences: A174359 A174360 A174361 * A174363 A174364 A174365

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 17 2010

Status

approved