A096342 Primes of the form p*q + p + q, where p and q are two successive primes.

11, 23, 47, 167, 251, 359, 479, 719, 1847, 2111, 2591, 3719, 6719, 7559, 8819, 10607, 12539, 14591, 19319, 27551, 29231, 31319, 51071, 53819, 68111, 97967, 149759, 155219, 172199, 177239, 195359, 199799, 234239, 273527, 305783, 314711, 339863

Offset: 1

Author

Giovanni Teofilatto, Jun 29 2004

Keywords

• nonn

Comments

a(n) == 3 mod 4.

Primes arising in A126148. - Jonathan Vos Post, Mar 08 2007

Number of primes <10^n: 0, 3, 8, 15, 26, 49, 99, 220, 514, 1228, 2991, 7746, 20218, 54081, ..., . - Robert G. Wilson v

Examples

			a(4)=167 because 11*13 + 11 + 13=167.
		

Links

• Vincenzo Librandi and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Librandi)

Crossrefs

Cf. A000040, A001043, A006094, A126148, A126199.

Programs

Mathematica

a = {}; Do[p = Prime[n]Prime[n + 1] + Prime[n] + Prime[n + 1]; If[ PrimeQ[p], AppendTo[a, p]], {n, 110}]; a (* Robert G. Wilson v, Jul 01 2004 *)
Select[Times@@#+Total[#]&/@Partition[Prime[Range[200]],2,1],PrimeQ] (* Harvey P. Dale, Nov 25 2018 *)

PARI

list(lim)=my(v=List(),p=2,t); forprime(q=3,, t=p*q+p+q; if (t>lim, return(Set(v))); if(isprime(t), listput(v,t)); p=q) \\ Charles R Greathouse IV, Sep 15 2015

Extensions

More terms from Robert G. Wilson v, Jul 02 2004