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Number of first half-quadrant Gaussian primes whose norm is less than 10^n.
3

%I #15 Feb 28 2020 04:37:27

%S 3,14,87,623,4818,39263,332406,2881124,25425200,227528084

%N Number of first half-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) = A091098(2n) + 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, x}]; 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), A091101, 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