A266163 Primes prime(k) such that (prime(k)*prime(k+1)+1)/2 is prime.

467, 2179, 2777, 4877, 6151, 6173, 6871, 7907, 7937, 8329, 9791, 11261, 11287, 12119, 12227, 12941, 13009, 14657, 14831, 15061, 15607, 16127, 16193, 16453, 16787, 16831, 17989, 18701, 18803, 18947, 19507, 20483, 20521, 20627, 22291, 22397, 22409, 22877, 23497

Offset: 1

Author

Robert Israel, Dec 22 2015

Keywords

• nonn

Comments

22397 and 22409 are first consecutive primes in this sequence. - Altug Alkan, Dec 22 2015

The next consecutive primes in this sequence are 134093 and 134129, 405541 and 405553, 432073 and 432097, 480803 and 480827, 586213 and 586237, ... - Harvey P. Dale, Dec 25 2015

Links

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

Crossrefs

Cf. A023524.

Programs

Magma

[p: p in PrimesInInterval(3,3*10^4) | IsPrime((p*NextPrime(p+1)+1) div 2)]; // Vincenzo Librandi, Dec 23 2015

Maple

lastp:= 3:
count:= 0:
while count < 100 do
  p:= nextprime(lastp);
  if isprime((lastp*p+1)/2) then
    count:= count+1;
    A[count]:= lastp;
  fi;
  lastp:= p;
od:
seq(A[i],i=1..100);

Mathematica

Prime@ Select[Range@ 2620, PrimeQ[(Prime@ # Prime[# + 1] + 1)/2] &] (* Michael De Vlieger, Dec 22 2015 *)
Transpose[Select[Partition[Prime[Range[50000]],2,1],PrimeQ[ (Times@@#+1)/2]&]] [[1]] (* Harvey P. Dale, Dec 25 2015 *)

PARI

lista(nn) = {forprime(p=3, nn, if(ispseudoprime((p*nextprime(p+1)+1)/2), print1(p, ", ")));} \\ Altug Alkan, Dec 22 2015