We discuss the summation of certain series defined by counting blocks of
digits in the B-ary expansion of an integer. For example, if s2(n) denotes
the sum of the base-2 digits of n, we show that ∑n≥1s2(n)/(2n(2n+1))=(γ+logπ4)/2. We recover this previous
result of Sondow in math.NT/0508042 and provide several generalizations.Comment: 12 pages, Introduction expanded, references added, accepted by J.
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