%I #10 Jan 12 2022 08:42:58
%S 5,13,29,53,97,173,181,229,257,277,281,293,337,617,733,757,809,881,
%T 953,1009,1093,1097,1217,1229,1237,1289,1373,1409,1481,1549,1709,1777,
%U 1801,1873,1901,2017,2029,2153,2213,2281,2381,2521,2633
%N Primes of the form x^2 + (y^3 + z^3)^2 with x,y,z > 0.
%C Merikoski proved that there are infinitely many primes of this form.
%H Charles R Greathouse IV, <a href="/A350687/b350687.txt">Table of n, a(n) for n = 1..10000</a>
%H 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.
%o (PARI) listA003325(lim)=my(v=List()); lim\=1; for(x=1, sqrtnint(lim-1, 3), my(x3=x^3); for(y=1, min(sqrtnint(lim-x3, 3), x), listput(v, x3+y^3))); Set(v)
%o list(lim)=lim\=1; my(v=List(),u=apply(sqr, listA003325(sqrtint(lim-1)))); for(x=1,sqrtint(lim-1), my(x2=x^2); for(i=1,#u, my(t=x2+u[i]); if(t>lim, break); if(isprime(t), listput(v,t)))); Set(v)
%Y Subsequence of A002144.
%Y Cf. A349900, A028916, A003325.
%K nonn
%O 1,1
%A _Charles R Greathouse IV_, Jan 11 2022