This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A225431 #41 Aug 19 2025 05:30:08
%S A225431 3,11,41,2131,110771,15558008491
%N A225431 Primes p such that there is a prime q satisfying 3*p^2 - q^2 = 2.
%C A225431 Primes q: 5, 19, 71, 3691, 191861,...
%C A225431 (q - p)/2: 1, 4, 15, 780, 40545,...
%C A225431 a(7) > 2.8016852867294*10^4857. - _Zak Seidov_, May 09 2013
%C A225431 Probably finite.
%C A225431 This is a form of Pell's equation with the requirement that solutions be prime. - _T. D. Noe_, May 14 2013
%H A225431 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/PellEquation.html">MathWorld: Pell Equation</a>
%e A225431 11 is prime and sqrt(3*11^2 - 2) = sqrt(361) = 19 is prime, so 11 is in the sequence.
%t A225431 nn = 1000; ta = LinearRecurrence[{4, -1}, {1, 3}, nn]; tb = LinearRecurrence[{4, -1}, {1, 5}, nn]; sol = Select[Range[nn], PrimeQ[ta[[#]]] && PrimeQ[tb[[#]]] &]; ta[[sol]] (* _T. D. Noe_, May 14 2013 *)
%o A225431 (PARI) v=[1,1]; for(i=1,1e4,v=[v[2],4*v[2]-v[1]]; if(ispseudoprime(v[2]) && ispseudoprime(sqrtint(3*v[2]^2-2)), print1(v[2]", "))) \\ _Charles R Greathouse IV_, May 13 2013
%o A225431 (PFGW)
%o A225431 ABC2 Linear(3,11,41,153,$a) & Linear(5,19,71,265,$a)
%o A225431 a: from 3 to 20000 // _Charles R Greathouse IV_, May 13 2013
%K A225431 nonn
%O A225431 1,1
%A A225431 _Irina Gerasimova_, May 07 2013
%E A225431 a(4) from _R. J. Mathar_, May 07 2013
%E A225431 a(6) from _Charles R Greathouse IV_, May 07 2013
%E A225431 a(5) from _Zak Seidov_, May 09 2013