[seqfan] A021085 and a constant derived from the primes.

[L. Edson Jeffery]

Re: https://oeis.org/A021085
    https://oeis.org/A000040

Some questions:

Let b(n) denote the n-th digit in the decimal expansion of

sum_{n=1..infinity} n/10^(n-1).

Does b(n) = A021085(n), for all n>0?

Similarly, let w(n) denote the n-th digit in the decimal expansion of

sum_{n=1..infinity} A000040(n)/10^(n-1),

where A000040 is the sequence of primes. If I have not miscalculated, then

w = {2,3,5,8,2,4,9,1,6,2,4,1,5,8,2,9,5,7,4,9,1,8,2,8...}.

Do there exist m such that w(m) = 0 and, if so, what is the offset (in w)
of the first occurrence, and is there any pattern to that sequence of m?

Ed Jeffery