1,2

All primes != 3 squared are of the form 3h+1 for some h. This follows from the fact that all primes != 3 are of the form 3j+1 or 3k+2 and squaring either of these leaves a number of the form 3h+1. So for primes < 10^n, squaring and summing gives a number equivelant to 9 + (3h+1)*(Pi(10^n)-1) = 9+3h*Pi(10^n)-3h + Pi(10^n)-1.

This implies that the sum of the squares of primes < 10^n mod 3 = Pi(10^n)-1 mod 3. While not foolproof, this is a way of checking the accuracy of the arithmetic performed by the generating program. For example Pi(10^13)-1 mod 3 = 0 and a(13) mod 3 = 0 would indicate the chances are good that the multiprecision routine performed as expected.

Cino Hilliard (hillcino368(AT)hotmail.com), Nov 23 2007, Table of n, a(n) for n = 1..14

Cino Hilliard, Gmp Demo Sum Primes Squared.

For n=1 the sum of the squares of the primes less than 10 is 2^2+3^2+5^2+7^2 = 87, the second entry in the sequence.

Sequence in context: A017803 A017750 A072692 this_sequence A033408 A109989 A147317

Adjacent sequences: A133388 A133389 A133390 this_sequence A133392 A133393 A133394

nonn

Cino Hilliard (hillcino368(AT)hotmail.com), Nov 23 2007