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

[israel at math.ubc.ca]

1)  Yes: sum_{n=1}^infinity n/10^(n-1) = 100/81.

b) The decimal expansion starts

2.358249162515829584918298249171625585162922492
582495896291825715838558298516316558918298250
3164969318962522958515922496258298989851651650
5692249238250
491783231630
...

I doubt that there is a discernable pattern.

Robert Israel


On Aug 26 2013, L. Edson Jeffery wrote:

>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
>
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