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

Author

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

Keywords

• nonn

Links

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

Crossrefs

Includes A174920.

Programs

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 *)