Summation of Series Defined by Counting Blocks of Digits
Loading...
Date
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
We discuss the summation of certain series defined by counting blocks of digits in the $B$-ary expansion of an integer. For example, if $s_2(n)$ denotes the sum of the base-2 digits of $n$, we show that $\sum_{n \geq 1} s_2(n)/(2n(2n+1)) = (γ+ \log \frac{4}π)/2$. We recover this previous result of Sondow in math.NT/0508042 and provide several generalizations.
12 pages, Introduction expanded, references added, accepted by J. Number Theory
12 pages, Introduction expanded, references added, accepted by J. Number Theory