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 A300587 #28 Mar 27 2018 17:21:11
%S A300587 1,2,3,3,4,5,6,5,7,7,6,8,8,9,10,10,8,11,11,10,11,13,10,12,14,15,13,15,
%T A300587 16,13,14,16,17,13,14,16,18,17,19,18,17,19,20,20,15,17,20,21,19,22,20,
%U A300587 23,21,19,20,24,23,24,18,19,25,22,25,23,26,26,22,27,26,20
%N A300587 Real part of the n-th Gaussian prime x + i*y, x >= y >= 0, ordered by norm x^2 + y^2.
%C A300587 With the restriction Re(z) >= Im(z) >= 0 used here and in A239621, there is exactly one Gaussian prime z for each possible norm |z|^2 in A055025. Sequence A239397 lists both, (x, y) and (y, x), for each of these having x > y (i.e., except for x = y = 1).
%C A300587 The nice graph shows that the values are denser towards the upper bound a(n) <= sqrt(A055025(n)) ~ sqrt(2n log n) than to the lower bound sqrt(A055025(n)/2) ~ sqrt(n log n), while for the imaginary parts A300588, i.e., min(Re(z),Im(z)), the distribution looks rather uniform.
%H A300587 M. F. Hasler, <a href="/A300587/b300587.txt">Table of n, a(n) for n = 1..10000</a>
%F A300587 a(n) = A239621(2n-1) = A239397(4n-2) (= A239397(4n-5) for n > 1).
%F A300587 a(n) = sqrt(A055025(n) - A300588(n)^2).
%o A300587 (PARI) c=1; for(n=1,oo, matsize(f=factor(n*I))[1]<=2 && vecsum(f[,2])==2+(f[1, 1]==I) && !write("/tmp/b300587.txt",c" "max(real(f=f[3-f[1,2],1]),imag(f))) && c++>1e4 && break) \\ Replace write("/tmp/b300587.txt",c" by print1(", to print the values.
%Y A300587 Odd bisection of A239621. See A300588 for imaginary parts, A055025 for the norms.
%K A300587 nonn,look
%O A300587 1,2
%A A300587 _M. F. Hasler_, Mar 09 2018