A154321 Primes p such that p, p^2 + 2p - 4 and p^2 + 8p - 4 are prime.

3, 5, 7, 13, 23, 167, 233, 277, 283, 383, 547, 607, 727, 733, 823, 1087, 1427, 1597, 1823, 2297, 3253, 3313, 3533, 3593, 3863, 4027, 4133, 4363, 6257, 6737, 7477, 7577, 7907, 9043, 9227, 11317, 11497, 11833, 11867, 12373, 12503, 12637, 12743, 13367

Offset

1,1

Links

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

Example

For p = 3, p^2 + 2p - 4 = 11, p^2 + 8p - 4 = 29;
for p = 7, p^2 + 2p - 4 = 59, p^2 + 8p - 4 = 101;
for p = 607, p^2 + 2p - 4 = 369659, p^2 + 8p - 4 = 373301.

Maple

a:= proc(n) if isprime(n) and isprime(n^2+2*n-4) and isprime(n^2+8*n-4) then n end if end proc: seq(a(n), n = 2 .. 15000); # Emeric Deutsch, Jan 20 2009

Mathematica

Select[Prime[Range[7000]], And@@PrimeQ/@{#^2 + 2 # - 4, #^2 + 8 # - 4}&] (* Vincenzo Librandi, Apr 18 2013 *)
Select[Prime[Range[2000]], AllTrue[#^2-4+{2#, 8#}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 29 2018 *)

Prog

(Magma) [p: p in PrimesUpTo(13500) | IsPrime(p^2+2*p-4) and IsPrime(p^2+8*p-4)]; // Vincenzo Librandi, Apr 18 2013

Crossrefs

Cf. A154319, A154320.

Sequence in context: A007658 A275175 A267549 * A024724 A024946 A257762

Adjacent sequences: A154318 A154319 A154320 * A154322 A154323 A154324

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 07 2009

Extensions

Corrected and extended by Emeric Deutsch, Jan 20 2009

Status

approved