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

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

Author

William Boyles, Jul 31 2016

Keywords

• nonn

Comments

Number of terms in A002313 that are less than A001105(n).

Links

• William Boyles, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001105, A002313.

Programs

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 *)

PARI

a(n)=my(s); forprime(p=2,2*n^2, if(p%4<3, s++)); s \\ Charles R Greathouse IV, Sep 02 2016