%I #19 Jul 10 2019 21:24:07

%S 3,26839,11,239,379

%N Smallest prime p such that there is a prime q satisfying (2*n + 1)*p^2 - (2*n-1)*q^2 = 2, or 0 if no such p exists.

%C Smallest prime p such that there is a prime q satisfying n*p^2 - (n-1)*q^2 = 1, or 0 if no such p exists: 5, 89,...

%C Primes p such that there is a prime q satisfying 5*p^2 - 3*q^2 = 2: 26839, 6391493137, 2540081 3820758542 5442608775 1898667220 6441480372 8945619713, ...

%C Primes q such that there is a prime p satisfying 5*p^2 - 3*q^2 = 2: 34649, 8251382159, 32792309 6359710073 4829167292 2880944251 7973351812 0308284159, ...

%C a(8) = 22656451 0158169057 8396614544 8202266647 1482614443 0220423848 3659973753 8209021958 1071702657 4442008471 0041419367 4411846431 - _Giovanni Resta_, May 16 2013

%C Conjecture: a(6) = a(7) = 0. _Charles R Greathouse IV_ reports that a(6) must have thousands of digits. - _Michael B. Porter_, May 19 2013

%H Eric Weisstein's World of Mathematics, <a href="http://www.mathworld.wolfram.com/PellEquation.html">Pell Equation</a>

%e (2*2+1)*26839^2 - (2*2-1)*34649^2 = 3601659605 - 3601659603 = 2 and 26839, 34649 are primes, so a(2) = 26839.

%Y Cf. A033313, A225431.

%K nonn

%O 1,1

%A _Irina Gerasimova_, May 16 2013

%E a(2) from _Giovanni Resta_, May 15 2013