[seqfan] Decimal expansion of sum of the reciprocals of the Mersenne primes
Jonathan Post
jvospost3 at gmail.com
Mon Mar 1 18:03:28 CET 2010
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?
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