A338836 Primes p such that 2*p^2-q^2 and 2*q^2-p^2 are prime, where q is the next prime after p.

53, 103, 397, 479, 1049, 1499, 1901, 1931, 2161, 2243, 2707, 3863, 4211, 5227, 5669, 6551, 6703, 7537, 8167, 8231, 8663, 8941, 9067, 9497, 10651, 10789, 10861, 12619, 14033, 14173, 14431, 14639, 14797, 15187, 15497, 16223, 16703, 17609, 18457, 18481, 20261, 21313, 21803, 22133, 22247, 22279

Offset

1,1

Links

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

Example

a(3)=397 is in the sequence because it is prime, the next prime is 401, and 2*397^2-401^2 = 154417 and 2*401^2-397^2 = 163993 are prime.

Maple

N:= 100: # for the first N terms
q:= 2: count:= 0: R:= NULL:
for iter from 1 while count < N do
  p:= q; q:= nextprime(q);
  if isprime(2*p^2-q^2) and isprime(2*q^2-p^2) then
    count:= count+1; R:= R, p;
  fi
od:
R;

Crossrefs

Sequence in context: A063363 A288619 A039476 * A061656 A141965 A141975

Adjacent sequences: A338833 A338834 A338835 * A338837 A338838 A338839

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Nov 11 2020

Status

approved