

A091100


Number of Gaussian primes whose norm is less than 10^n.


3



16, 100, 668, 4928, 38404, 313752, 2658344, 23046512, 203394764, 1820205436, 16472216912, 150431552012, 1384262129028, 12819767598972, 119378281788240, 1116953361826164
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..16.
Marc Deléglise, Pierre Dusart, and XavierFrancois Roblot, Counting primes in residue classes, Math. Comp. 73 (2004), no. 247, 15651575
Eric Weisstein's World of Mathematics, Gaussian Prime
Index entries for Gaussian integers and primes


FORMULA

a(2n) = 8*A091098(2n) + 4*A091099(n) + 4.
a(n) ~ 4 Li(10^n) ~ k/n * 10^n, where k = 4/log(10) = 1.737....  Charles R Greathouse IV, Oct 24 2012


MATHEMATICA

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, lim1, lim1}, {y, lim1, lim1}]; cnt, {n, 6}]


CROSSREFS

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.
Cf. A091134 (number of Gaussian primes whose modulus is less than 10^n).
Cf. A017934, A295996.
Sequence in context: A169721 A125326 A126484 * A061432 A115328 A223767
Adjacent sequences: A091097 A091098 A091099 * A091101 A091102 A091103


KEYWORD

nonn


AUTHOR

T. D. Noe, Dec 19 2003


EXTENSIONS

a(10)a(16) from Seiichi Manyama using the data in A091098, Dec 03 2017


STATUS

approved



