A327700 Primes p such that p + q*(q-p) and q + p*(q-p) are prime, where q is the next prime after p.

2, 3, 5, 23, 59, 61, 83, 151, 233, 263, 269, 293, 373, 401, 433, 503, 541, 619, 701, 971, 1103, 1433, 1493, 1601, 1621, 1861, 1949, 2099, 2179, 2371, 2441, 2543, 2741, 2851, 2903, 2999, 3083, 3181, 3313, 3413, 3559, 3631, 4073, 4093, 4549, 4591, 4643, 5039, 5081, 5471, 5711, 5749

Offset

1,1

Links

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

Maple

R:= NULL: count:= 0:
q:= 2:
do
  p:= q; q:= nextprime(p);
  if isprime(p+(q-p)*q) and isprime(q+(q-p)*p) then
     count:= count+1;
     R:= R, p;
     if count = 100 then break fi
  fi
od:
R;

Mathematica

Do[a=Prime[k]+Prime[k+1]*(Prime[k+1]-Prime[k]); b=Prime[k+1]+Prime[k]*(Prime[k+1]-Prime[k]); If[PrimeQ[a]&&PrimeQ[b], Print[Prime[k]]], {k, 1, 757}] (* Metin Sariyar, Sep 23 2019 *)
chpQ[{a_, b_}]:=AllTrue[{a+b(b-a), b+a(b-a)}, PrimeQ]; Select[Partition[ Prime[ Range[800]], 2, 1], chpQ][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 05 2021 *)

Crossrefs

Includes A174920.

Sequence in context: A080016 A171432 A214703 * A182976 A042363 A208220

Adjacent sequences: A327697 A327698 A327699 * A327701 A327702 A327703

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Sep 22 2019

Status

approved