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A275534
Number of primes of the form x^2 + y^2 less than or equal to 2*n^2.
1
1, 2, 4, 5, 7, 9, 12, 15, 18, 22, 25, 29, 33, 37, 43, 46, 51, 56, 62, 68, 75, 79, 86, 93, 102, 107, 114, 119, 127, 136, 143, 150, 160, 169, 179, 184, 195, 206, 215, 223, 233, 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
OFFSET
1,2
COMMENTS
Number of terms in A002313 that are less than A001105(n).
LINKS
MATHEMATICA
nn = 66; Table[Count[Take[#, PrimePi[2 n^2]], k_ /; k > 0], {n, nn}] &@
SquaresR[2, Prime@ Range@ PrimePi[2 nn^2]] (* Michael De Vlieger, Aug 01 2016 *)
PROG
(C++)
#include <iostream>
#include <cmath>
using namespace std;
bool IsPrime(int a){
int i = 3;
if(a == 2)
{return true; }
if(a <= 1 || a%2 == 0)
{return false; }
else{
while(i <= sqrt(a)){
if(a%i == 0)
{return false; }
else
{i = i+2; }}
return true; }}
int main(){
int Max, FourKPlusOne;
int limit=25; //Number of terms
for(int TermNum=1; TermNum<=limit; TermNum++){
Max = 2*TermNum*TermNum;
int Term=1;
for(int counter3=1; counter3<=(Max-1)/4; counter3++){
FourKPlusOne=((4*(counter3))+1);
if(IsPrime(FourKPlusOne) == true && FourKPlusOne<=Max)
{Term++; }}
cout<<Term<<endl; }}
(PARI) a(n)=my(s); forprime(p=2, 2*n^2, if(p%4<3, s++)); s \\ Charles R Greathouse IV, Sep 02 2016
CROSSREFS
Sequence in context: A062428 A250000 A056833 * A069355 A212661 A288511
KEYWORD
nonn
AUTHOR
William Boyles, Jul 31 2016
STATUS
approved