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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
OFFSET
1,1
LINKS
Marc Deléglise, Pierre Dusart, and Xavier-Francois Roblot, Counting primes in residue classes, Math. Comp. 73 (2004), no. 247, 1565-1575
Eric Weisstein's World of Mathematics, Gaussian Prime
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).
Sequence in context: A169721 A125326 A126484 * A061432 A376705 A115328
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