A091101 - OEIS

A091101

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

5, 27, 173, 1245, 9635, 78525, 664811, 5762247, 50850399, 455056167

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, Gaussian Prime

Index entries for Gaussian integers and primes

FORMULA

a(2n) = 2*A091098(2n) + 2*A091099(n) + 1.

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, 0, lim1}, {y, 0, 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), A091100, A091102.

Sequence in context: A225344 A109963 A201870 * A185622 A225309 A231091

Adjacent sequences: A091098 A091099 A091100 * A091102 A091103 A091104

KEYWORD

nonn,more

AUTHOR

T. D. Noe, Dec 19 2003

EXTENSIONS

a(10) calculated from the data at A091098 and A091099 by Amiram Eldar, Feb 28 2020

STATUS

approved