A131590 Sum of the squares of the first 2^n primes.

4, 13, 87, 1027, 13275, 155995, 1789395, 19523155, 204330315, 2081006083, 20605602003, 199966727443, 1908356153955, 17942429101363, 166591116531123, 1529578004981731, 13917470067182067, 125565110929591171, 1124685106917162579, 10009134886727192611

Offset: 0

Author

Cino Hilliard, Aug 30 2007

Keywords

• nonn

Examples

			The sum of the squares of the first 2^2 primes is a(2) = 4 + 9 + 25 + 49 = 87.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..34 (terms 0..30 from Michael S. Branicky)

Crossrefs

Cf. A024450, A099825.

Programs

Mathematica

Array[Total[Prime[Range[2^#]]^2]&,20,0] (* James C. McMahon, Feb 25 2025 *)

PARI

sumprimesq(n,b) = { local(x,y,s,a); for(y=0,n, s=0; for(x=1,b^y, s+=prime(x)^2; ); print1(s","); ) }

PARI

lista(pmax) = {my(s = 0, k = 0, pow = 1); forprime(p = 1, pmax, k++; s += p^2; if(k == pow, print1(s, ", "); pow *= 2));} \\ Amiram Eldar, Jul 06 2024

Python

from sympy import sieve, prime
def a(n): return sum(p*p for p in sieve.primerange(1, prime(2**n)+1))
print([a(n) for n in range(20)]) # Michael S. Branicky, Apr 13 2021

Formula

a(n) = A024450(2^n). - Amiram Eldar, Jul 06 2024

Extensions

a(18) and beyond from Michael S. Branicky, Apr 13 2021