[seqfan] Decimal expansion of sum of the reciprocals of the Mersenne primes

[Jonathan Post]

I do not see in OEIS either the Decimal expansion nor continued
fraction representations
SUM[i=1..infinity] 1/A000668(i) =  SUM[i=1..infinity] reciprocal of
i-th Mersenne prime (primes of form 2^p - 1 where p is a prime)

(1/3) + (1/7) + (1/31) + (1/127) + (1/8191) + (1/131071) +  (1/524287) + ...

We know it to be strictly less than the Erdős-Borwein constant,which,
is the sum of the reciprocals of the Mersenne numbers.

The crudest calculation (using Google as a low-precision calculator) gives
(1/3) + (1/7) + (1/31) + (1/127) + (1/8191) + (1/131071) ~ 0.516452271

Have I missed it as a seq, or is it worth doing to 100 digits as a new seq?