A180932 Primes of the form pq + p + 1 where p < q are adjacent primes.

19, 41, 457, 691, 929, 2539, 3181, 3659, 6637, 19181, 29059, 32579, 55921, 57839, 60733, 71011, 83203, 123547, 127081, 132113, 149371, 154823, 176819, 181873, 194917, 245501, 320911, 382541, 430981, 497711, 510481, 523433, 549817, 595207

Offset: 1

Author

Carmine Suriano, Sep 26 2010

Keywords

• nonn

Comments

In the sequence of first differences D(9) = 12544 is the square of 112.

In the sequence of second differences DD(3) = 4 and DD(7) = 2500 are squares.

Examples

			a(7) = 3181 since 3181 = 53*(59+1) + 1 where 53 and 59 are successive primes.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A180931.

Primes in A286624.

Programs

Magma

[a: n in [0..200] | IsPrime(a) where a is NthPrime(n)*NthPrime(n+1)+NthPrime(n)+1]; // Vincenzo Librandi, Jul 07 2017

Mathematica

Select[Times@@#+#[[1]]+1&/@Partition[Prime[Range[200]],2,1],PrimeQ] (* Harvey P. Dale, Apr 26 2014 *)

PARI

p=2;forprime(q=3,1e3,k=p*(q+1)+1;if(isprime(k),print1(k","));p=q) \\ Charles R Greathouse IV, Sep 27 2010

Extensions

New description and editing from Charles R Greathouse IV, Sep 27 2010