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

1,1

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.

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A180931.

Primes in A286624.

Sequence in context: A323387 A328493 A225583 * A140603 A139580 A156897

Adjacent sequences: A180929 A180930 A180931 * A180933 A180934 A180935

Keyword

nonn

Author

Carmine Suriano, Sep 26 2010

Extensions

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

Status

approved