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%I #23 Sep 02 2016 00:16:16
%S 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 102,107,114,119,127,136,143,150,160,169,179,184,195,206,215,223,233,
%U 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 Number of primes of the form x^2 + y^2 less than or equal to 2*n^2.
%C Number of terms in A002313 that are less than A001105(n).
%H William Boyles, <a href="/A275534/b275534.txt">Table of n, a(n) for n = 1..1000</a>
%t nn = 66; Table[Count[Take[#, PrimePi[2 n^2]], k_ /; k > 0], {n, nn}] &@
%t SquaresR[2, Prime@ Range@ PrimePi[2 nn^2]] (* _Michael De Vlieger_, Aug 01 2016 *)
%o (C++)
%o #include <iostream>
%o #include <cmath>
%o using namespace std;
%o bool IsPrime(int a){
%o int i = 3;
%o if(a == 2)
%o {return true;}
%o if(a <= 1 || a%2 == 0)
%o {return false;}
%o else{
%o while(i <= sqrt(a)){
%o if(a%i == 0)
%o {return false;}
%o else
%o {i = i+2;}}
%o return true;}}
%o int main(){
%o int Max, FourKPlusOne;
%o int limit=25; //Number of terms
%o for(int TermNum=1; TermNum<=limit; TermNum++){
%o Max = 2*TermNum*TermNum;
%o int Term=1;
%o for(int counter3=1; counter3<=(Max-1)/4; counter3++){
%o FourKPlusOne=((4*(counter3))+1);
%o if(IsPrime(FourKPlusOne) == true && FourKPlusOne<=Max)
%o {Term++;}}
%o cout<<Term<<endl;}}
%o (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 Cf. A001105, A002313.
%K nonn
%O 1,2
%A _William Boyles_, Jul 31 2016
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