Calculating R values by convolution

Let P be the polynomial
x + x³ + x⁵ + x⁷+ x¹¹+ x¹³ + x¹⁷ + ...
whose exponents are the primes, and consider Q = P². The coefficient of x^q in Q will be sum(i= 0 .. q) (a_i a_q-i) where the a_i are the coefficients in P, and in particular are zero when i is not prime and one when it is. So the product is one if and only if i and q-i are both prime, in which case qis the sum of two primes. Since we sum over all i from zero toq, the coefficient of xⁿwill be R(n).

If we consider only a truncated version of the polynomial P, say going up to x^2m+1, we will get correct values of R(n) only up to n=2m+2. So we have to consider extremely long values.

visualisation of the function!