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A180932 Primes of the form pq + p + 1 where p < q are adjacent primes. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 2 19:18 EST 2021. Contains 341756 sequences. (Running on oeis4.)