2^(a(2n)-1)-1 predicts the number of pair_solutions of even length L for AB = A^2 + B^2. For instance with length 18 we have 10^18 + 1 = 101.9901.999999000001 or 3 divisors F which when put into the Mersenne formula 2^(F-1)-1 yields 3 pairs (see reference 'Puzzle 104' for details).