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 A262340 #11 Feb 16 2025 08:33:27
%S A262340 5,41,137,281,617,857,977,1097,1217,1321,1657,1697,2137,4217,4457,
%T A262340 4937,5297,6257,6337,7537,7577,7817,7937,9137,10009,10169,10289,10337,
%U A262340 10457,10529,11369,11497,11681,11897,12809,13177,13721,14489,15329,16889,17417
%N A262340 Primes of the form p^2 + b^4 where p is a prime.
%C A262340 It is not known whether there are infinitely many primes of such form.
%C A262340 Same as the intersection of A185086 (primes of the form p^2 + k^2 where p is a prime) with A028916 (primes of the form a^2 + b^4). (Proof: Clearly, p^2 + b^4 is in A185086 and in A028916. Conversely, if a(n) = p^2 + k^2 = a^2 + b^4, then by the uniqueness part of Fermat's two squares (or 4n+1) theorem, (p,k) = (a,b^2) or (p,k) = (b^2,a). But the latter is impossible since p is prime, so a(n) = p^2 + b^4.)
%H A262340 Charles R Greathouse IV, <a href="/A262340/b262340.txt">Table of n, a(n) for n = 1..10000</a>
%H A262340 Art of Problem Solving, <a href="http://www.artofproblemsolving.com/wiki/index.php/Fermat's_Two_Squares_Theorem">Fermat's Two Squares Theorem</a>
%H A262340 MathWorld, <a href="https://mathworld.wolfram.com/Fermats4nPlus1Theorem.html">Fermat's 4n+1 Theorem</a>
%e A262340 5 = 2^2 + 1^4, so a(1) = 5.
%t A262340 nn = 14; Union[ Flatten[ Table[ Select[ Prime[n]^2 + Range[nn]^4, PrimeQ[#] && # < nn^4 &], {n,PrimePi[nn^2]}]]]
%o A262340 (PARI) list(lim)=my(v=List(),p2,t); forprime(p=2,sqrtint(lim\=1), p2=p^2; forstep(x=1+p%2,sqrtnint(lim-p2,4),2, if(isprime(t=p2+x^4), listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Aug 21 2017
%Y A262340 Cf. A028916, A185086.
%K A262340 nonn
%O A262340 1,1
%A A262340 _Jonathan Sondow_, Oct 03 2015