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

1,1

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A139834 A100558 A126199 * A066179 A217566 A347141

Adjacent sequences: A096339 A096340 A096341 * A096343 A096344 A096345

Keyword

nonn

Author

Giovanni Teofilatto, Jun 29 2004

Extensions

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

Status

approved