0,1

Except for the first term, these numbers are divisible by 3. This follows from the fact that all primes are of the form 3m+1 or 3m+2 and the square of either of these forms is of the form 3h+1.

Then for the first 10 primes, the sum of the squares becomes 4+9+3h*8+8 = 21+3h*8, which is divisible by 3.

By induction, assuming that the sum of the squares of the first 10^n primes is divisible by 3, then the difference between the sum for n+1 and the sum for n is (3*h+1)*(10^(n+1) - 10^n) = (3*h+1)*(9*10^n), which is divisible by 3. [Comments corrected by Paul Schumacher (schumach(AT)math.tamu.edu), Mar 16 2008]

C. Hilliard, SumprimesGmpSq.

The sum of squares of the first 10^1 primes = 2397, the second entry in the sequence.

(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", "); ) }

Sequence in context: A097476 A047676 A079187 this_sequence A066850 A066837 A132639

Adjacent sequences: A131584 A131585 A131586 this_sequence A131588 A131589 A131590

nonn

Cino Hilliard (hillcino368(AT)hotmail.com), Aug 29 2007, Oct 25 2007