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A275534 Number of primes of the form x^2 + y^2 less than or equal to 2*n^2.

%I A275534 #23 Sep 02 2016 00:16:16
%S A275534 1,2,4,5,7,9,12,15,18,22,25,29,33,37,43,46,51,56,62,68,75,79,86,93,
%T A275534 102,107,114,119,127,136,143,150,160,169,179,184,195,206,215,223,233,
%U A275534 242,254,264,274,285,297,307,318,330,339,350,362,376,386,400,415,428,441,452,465,483,498,510,525,541
%N A275534 Number of primes of the form x^2 + y^2 less than or equal to 2*n^2.
%C A275534 Number of terms in A002313 that are less than A001105(n).
%H A275534 William Boyles, <a href="/A275534/b275534.txt">Table of n, a(n) for n = 1..1000</a>
%t A275534 nn = 66; Table[Count[Take[#, PrimePi[2 n^2]], k_ /; k > 0], {n, nn}] &@
%t A275534 SquaresR[2, Prime@ Range@ PrimePi[2 nn^2]] (* _Michael De Vlieger_, Aug 01 2016 *)
%o A275534 (C++)
%o A275534 #include <iostream>
%o A275534 #include <cmath>
%o A275534 using namespace std;
%o A275534 bool IsPrime(int a){
%o A275534     int i = 3;
%o A275534     if(a == 2)
%o A275534     {return true;}
%o A275534     if(a <= 1 || a%2 == 0)
%o A275534     {return false;}
%o A275534     else{
%o A275534         while(i <= sqrt(a)){
%o A275534             if(a%i == 0)
%o A275534             {return false;}
%o A275534             else
%o A275534             {i = i+2;}}
%o A275534     return true;}}
%o A275534 int main(){
%o A275534     int Max, FourKPlusOne;
%o A275534     int limit=25;            //Number of terms
%o A275534     for(int TermNum=1; TermNum<=limit; TermNum++){
%o A275534         Max = 2*TermNum*TermNum;
%o A275534         int Term=1;
%o A275534         for(int counter3=1; counter3<=(Max-1)/4; counter3++){
%o A275534             FourKPlusOne=((4*(counter3))+1);
%o A275534             if(IsPrime(FourKPlusOne) == true && FourKPlusOne<=Max)
%o A275534             {Term++;}}
%o A275534         cout<<Term<<endl;}}
%o A275534 (PARI) a(n)=my(s); forprime(p=2,2*n^2, if(p%4<3, s++)); s \\ _Charles R Greathouse IV_, Sep 02 2016
%Y A275534 Cf. A001105, A002313.
%K A275534 nonn
%O A275534 1,2
%A A275534 _William Boyles_, Jul 31 2016