|
%I #15 Feb 28 2020 04:32:25
%S 5,27,173,1245,9635,78525,664811,5762247,50850399,455056167
%N Number of first-quadrant Gaussian primes whose norm is less than 10^n.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GaussianPrime.html">Gaussian Prime</a>
%H <a href="/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>
%F a(2n) = 2*A091098(2n) + 2*A091099(n) + 1.
%t Table[lim2=10^n; lim1=Floor[Sqrt[lim2]]; cnt=0; Do[If[x^2+y^2<lim2&&PrimeQ[x+I y, GaussianIntegers->True], cnt++ ], {x, 0, lim1}, {y, 0, lim1}]; cnt, {n, 6}]
%Y Cf. A091098 (number of primes of the form 4k+1 less than 10^n), A091099 (number of primes of the form 4k+3 less than 10^n), A091100, A091102.
%K nonn,more
%O 1,1
%A _T. D. Noe_, Dec 19 2003
%E a(10) calculated from the data at A091098 and A091099 by _Amiram Eldar_, Feb 28 2020
|
