A131590 - OEIS

%I #21 Jul 06 2024 04:41:53

%S 4,13,87,1027,13275,155995,1789395,19523155,204330315,2081006083,

%T 20605602003,199966727443,1908356153955,17942429101363,

%U 166591116531123,1529578004981731,13917470067182067,125565110929591171,1124685106917162579,10009134886727192611

%N Sum of the squares of the first 2^n primes.

%H Amiram Eldar, <a href="/A131590/b131590.txt">Table of n, a(n) for n = 0..34</a> (terms 0..30 from Michael S. Branicky)

%F a(n) = A024450(2^n). - _Amiram Eldar_, Jul 06 2024

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

%o (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","); ) }

%o (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

%o (Python)

%o from sympy import sieve, prime

%o def a(n): return sum(p*p for p in sieve.primerange(1, prime(2**n)+1))

%o print([a(n) for n in range(20)]) # _Michael S. Branicky_, Apr 13 2021

%Y Cf. A024450, A099825.

%K nonn

%O 0,1

%A _Cino Hilliard_, Aug 30 2007

%E a(18) and beyond from _Michael S. Branicky_, Apr 13 2021