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 A349900 #10 Jan 12 2022 08:42:42 %S A349900 5,13,17,29,37,41,53,61,89,101,109,149,173,181,197,229,257,269,281, %T A349900 293,349,353,389,401,433,461,509,541,577,601,613,677,701,733,757,773, %U A349900 797,809,829,941,1049,1061,1093,1117,1181,1229,1297,1301 %N A349900 Primes of the form x^2 + (y^2+1)^2. %C A349900 Merikoski proved that there are infinitely many primes of this form, and that the order of growth of the sequence up to x is x^(3/4)/log x. (His method did not provide enough Type II information to prove that there is a C such that there are ~ C*x^(3/4)/log x.) %H A349900 Charles R Greathouse IV, <a href="/A349900/b349900.txt">Table of n, a(n) for n = 1..10000</a> %H A349900 Jori Merikoski, <a href="https://arxiv.org/abs/2112.03617">The polynomials X^2+(Y^2+1)^2 and X^2+(Y^3+Z^3)^2 also capture their primes</a>, arXiv:2112.03617 [math.NT], 2021. %F A349900 a(n) ≍ (n log n)^(4/3). %o A349900 (PARI) list(lim)=my(v=List()); lim\=1; for(y=0,sqrtint(sqrtint(lim-1)-1), my(t=(y^2+1)^2); forstep(x=2-y%2,sqrtint(lim-t),2, my(p=x^2+t); if(isprime(p), listput(v,p)))); Set(v) %o A349900 (PARI) is(n)=if(n<5 || !isprime(n), return(0)); for(y=0,sqrtint(sqrtint(n-1)-1), if(isprime(n-(y^2+1)^2), return(1))); 0 %Y A349900 Subsequence of A002144. %Y A349900 Cf. A028916, A350687. %K A349900 nonn %O A349900 1,1 %A A349900 _Charles R Greathouse IV_, Jan 11 2022