A153645 Primes p such that p^2 + 4 and p^2 + 4p + 2 are also prime.

3, 5, 7, 13, 17, 47, 67, 73, 137, 167, 277, 307, 313, 487, 503, 593, 607, 613, 787, 823, 1117, 1123, 1237, 1523, 1543, 1637, 1987, 2777, 2887, 3037, 3163, 3433, 3457, 3463, 3797, 3853, 4093, 4283, 4583, 5113, 5297, 5323, 5683, 5953, 6047, 6577, 6803, 6823

Offset

1,1

Comments

Subsequence of A062324.

Links

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

Example

For prime p = 3, p^2+4 = 13 and p^2+4p+2 = 23 are prime; for p = 67, p^2+4 = 4493 and p^2+4p+2 = 4759 are prime.

Maple

a := proc (n) if isprime(n) = true and isprime(n^2+4) = true and isprime(n^2+4*n+2) = true then n else end if end proc: seq(a(n), n = 1 .. 7000); # Emeric Deutsch, Jan 02 2009

Mathematica

Select[Prime[Range[10000]], PrimeQ[#^2+4]&&PrimeQ[#^2 +4#+2]&] (* Vincenzo Librandi, Jul 27 2012 *)

Prog

(Magma) [ p: p in PrimesUpTo(7000) | IsPrime(p^2+4) and IsPrime(p^2+4*p+2) ];

Crossrefs

Cf. A062324 (p and p^2+4 are both prime).

Sequence in context: A226794 A300748 A173641 * A106878 A192294 A227531

Adjacent sequences: A153642 A153643 A153644 * A153646 A153647 A153648

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 30 2008

Extensions

Edited, corrected (three terms deleted) and extended beyond a(10) by Klaus Brockhaus, Jan 02 2009

Corrected and extended by Emeric Deutsch, Jan 02 2009

Status

approved