A152292 Primes p of the form : (p-n)/(n+1)=prime and (n+1)*p+n=prime. n=2.

17, 23, 59, 89, 239, 269, 293, 383, 419, 503, 953, 1013, 1193, 1259, 1823, 1979, 2129, 2633, 2789, 3209, 3389, 4229, 5099, 5333, 6089, 6299, 6803, 7019, 7673, 7853, 8123, 8513, 8753, 8819, 9059, 9203, 10169, 10223, 10589, 10853, 10979, 11159, 12689

Offset

1,1

Comments

This is the general form : (p-n)/(n+1)=prime and (n+1)*p+n=prime; 'Safe' primes and 'Sophie Germain' primes just one part of this general form; If n=1 then we got 'Safe' primes and 'Sophie Germain' primes.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

Res:= NULL: count:= 0:
q:= 1:
while count < 100 do
q:= nextprime(q);
if isprime(3*q+2) and isprime(9*q+8)
    then Res:= Res, 3*q+2; count:= count+1
  fi
od:
Res; # Robert Israel, Mar 07 2018

Mathematica

lst={}; n=2; Do[p=Prime[k]; If[PrimeQ[(p-n)/(n+1)]&&PrimeQ[(n+1)*p+n], AppendTo[lst, p]], {k, 7!}]; lst

Prog

(PARI) lista(nn) = forprime(p=17, nn, if(isprime(3*p+2) && isprime(p\3), print1(p", "))); \\ Altug Alkan, Mar 07 2018
(Magma) [NthPrime(n): n in [5..2*10^3] | IsPrime(NthPrime(n) div 3) and IsPrime(3*NthPrime(n)+2)]; // Vincenzo Librandi, Mar 08 2018

Crossrefs

Cf. A059455, A152293, A152294, A152295, A152388.

Sequence in context: A126329 A130098 A046123 * A214493 A039319 A043142

Adjacent sequences: A152289 A152290 A152291 * A152293 A152294 A152295

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 02 2008

Status

approved