login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A062711 Number of prime Gaussian integers z=a+bi with |z|<=n. 4
0, 1, 4, 6, 8, 10, 15, 19, 21, 25, 32, 34, 38, 44, 46, 52, 60, 66, 73, 79, 87, 93, 98, 104, 114, 122, 128, 138, 146, 154, 163, 173, 181, 193, 203, 213, 221, 231, 239, 245, 259, 273, 280, 294, 304, 316, 327, 343, 359, 369 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

Index entries for Gaussian integers and primes

FORMULA

Two prime Gaussian integers are not counted separately if they are associated, i.e. if their quotient is a unit (1, i, -1 or -i).

Similar to the ordinary prime number theorem (see A000720) we have the asymptotic expression: a(n) ~ n^2/(2 * log(n)) - Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 16 2001

a(1)=0, a(n)=1+A066339(n^2)+A066490(n) for n>0 - T. D. Noe, Feb 20 2007

MATHEMATICA

m = 50;

t = Table[x + y I, {x, -m, m}, {y, -m, m}] // Flatten[#, 1]& // Select[#, PrimeQ[#, GaussianIntegers -> True]& ]& // Sort // DeleteDuplicates[#, Abs[#1] == Abs[#2] && MatchQ[#1 /#2 , 1|-1|I|-I]& ]&;

a[n_] := Select[t, Abs[#] <= n&] // Length;

Array[a, m] (* Jean-Fran├žois Alcover, Jul 29 2016 *)

CROSSREFS

Cf. A000328, A062327, A000720.

Sequence in context: A161344 A127792 A288814 * A280739 A117347 A088011

Adjacent sequences:  A062708 A062709 A062710 * A062712 A062713 A062714

KEYWORD

nonn,nice

AUTHOR

Reiner Martin (reinermartin(AT)hotmail.com), Jul 14 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 13 02:59 EST 2019. Contains 329085 sequences. (Running on oeis4.)