A154552 Greater of two consecutive primes, p < q, such that both p*q+p-q and p*q-p+q are prime numbers.

3, 5, 29, 509, 997, 1399, 1627, 3307, 4217, 5477, 5689, 6569, 6599, 7369, 7393, 7841, 8191, 8861, 10067, 11311, 11801, 13859, 14401, 15859, 16987, 17851, 18211, 20593, 21101, 24169, 25013, 25339, 25621, 26209, 28019, 28409, 28439, 32009, 35677

Offset

1,1

Comments

3*5-2=13; 3*5+2=17, 23*29-6=661; 23*29+6=673...

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

p:= 1: q:= 2: Res:= NULL:
while q < 100000 do
  p:= q; q:= nextprime(q);
  if isprime(p*q+p-q) and isprime(p*q+q-p) then
    Res:= Res, q;
  fi
od:
Res; # Robert Israel, May 10 2017

Mathematica

lst={}; Do[pp=Prime[n-1]; p=Prime[n]; d=p-pp; If[PrimeQ[pp*p-d]&&PrimeQ[pp*p+d], AppendTo[lst, p]], {n, 2, 8!}]; lst
pqpQ[{p_, q_}]:=Module[{pq=p*q}, And@@PrimeQ[{pq+p-q, pq-p+q}]]; Transpose[ Select[Partition[Prime[Range[4000]], 2, 1], pqpQ]][[2]] (* Harvey P. Dale, May 20 2012 *)

Prog

(PARI) is(n)=my(p); isprime(n) && isprime((p=precprime(n-1))*n+p-n) && isprime(p*n-p+n) \\ Charles R Greathouse IV, May 10 2017

Crossrefs

Cf. A138111, A138170, A154550, A154551.

Sequence in context: A283266 A060255 A316791 * A261463 A352913 A100857

Adjacent sequences: A154549 A154550 A154551 * A154553 A154554 A154555

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 11 2009

Extensions

Edited by Omar E. Pol, Jan 12 2009

Status

approved