A237812 Primes p such that 2*p+1 and 2*p+13 are also prime.

2, 3, 5, 23, 29, 83, 89, 113, 173, 233, 239, 293, 509, 653, 719, 743, 1013, 1049, 1223, 1289, 1499, 2003, 2039, 2063, 2129, 2339, 2393, 2459, 2543, 2693, 2753, 2819, 2963, 3389, 3449, 4409, 4733, 4919, 5039, 6053, 6113, 6263, 6323, 6329, 6449, 7433, 7643

Offset

1,1

Links

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

Example

23 is in the sequence because 23, 2*23+1 = 47 and 2*23+13 = 59 are all prime.

Mathematica

Select[Prime[Range[10000]], PrimeQ[2 # + 1] && PrimeQ[2 # + 13] &] (* Vincenzo Librandi, Feb 15 2014 *)
Select[Prime[Range[1000]], AllTrue[2#+{1, 13}, PrimeQ]&] (* Harvey P. Dale, Jun 27 2023 *)

Prog

(PARI) s=[]; forprime(p=2, 10000, if(isprime(2*p+1) && isprime(2*p+13), s=concat(s, p))); s
(Magma) [p: p in PrimesUpTo(9200) | IsPrime(2*p+1) and IsPrime(2*p+13)]; // Vincenzo Librandi, Feb 15 2014

Crossrefs

Cf. A126107, A237810, A237811, A237813, A237814.

Sequence in context: A122004 A023231 A034470 * A138170 A105885 A228830

Adjacent sequences: A237809 A237810 A237811 * A237813 A237814 A237815

Keyword

nonn

Author

Colin Barker, Feb 13 2014

Status

approved