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 A057368 #19 Apr 03 2022 01:30:28
%S A057368 1,1,2,1,2,2,2,3,1,4,3,1,4,3,3,3,4,3,5,6,2,4,6,3,7,6,4,4,4,4,8,6,5,6,
%T A057368 8,5,6,7,3,9,5,5,9,8,7,9,7,7,10,8,6,9,10,5,8,8,6,10,12,8,11,10,6,9,15,
%U A057368 5,11,11,4,11,14,6,12,10,12,11,9,8,12,19,10,15,10,8,19,11,8,11,14,15,13
%N A057368 Number of Gaussian primes (in the first half-quadrant; i.e., 0 to 45 degrees) with real part = n.
%C A057368 Conjecture: a(n) > 0 for all n > 0. - _Franklin T. Adams-Watters_, May 05 2006
%C A057368 The graph of this sequence inspires the following conjecture: A > a(n)/pi(n) > B, where A and B are constants and pi(n) is the prime counting function (A000720). - _T. D. Noe_, Feb 26 2007
%C A057368 Stronger conjecture: Let pi(n) be the prime counting function (A000720). Then pi(n) >= a(n) >= pi(n)/5 for n>1, with the following equalities: pi(2)=a(2), pi(3)=a(3), pi(10)=a(10) and a(12)=pi(12)/5. - _T. D. Noe_, Feb 26 2007
%D A057368 Mark A. Herkommer, "Number Theory, A Programmer's Guide," McGraw-Hill, New York, 1999, page 269.
%H A057368 T. D. Noe, <a href="/A057368/b057368.txt">Table of n, a(n) for n = 1..10000</a>
%H A057368 <a href="/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>
%F A057368 a(n) = A069004(n) + 1 if n is 1 or a prime = 3 (mod 4), A069004(n) otherwise. - _Franklin T. Adams-Watters_, May 05 2006
%F A057368 a(n) = O(n/log(n)). - _Thomas Ordowski_, Mar 06 2017
%t A057368 Do[ c=0; Do[ If[ PrimeQ[ j + k*I, GaussianIntegers -> True ], c++ ], {j, n, n}, {k, 0, j} ]; Print[ c ], {n, 1, 75} ]
%Y A057368 Cf. A055683 and A057352.
%Y A057368 Cf. A069004.
%K A057368 nonn
%O A057368 1,3
%A A057368 _Robert G. Wilson v_, Sep 22 2000
%E A057368 More terms from _Franklin T. Adams-Watters_, May 05 2006