[Author]
Minabutdinov Aleksey R.
[Title]
$q$-weighted analogue of the Trollope-Delange formula
[AMS Subj-class]
11A63 Radix representation; digital problems
39B22 Equations for real functions
[Keywords]
$q$-weighted Trollope-Delange formula, Takagi-Landsberg curve
[Abstract]
Let $s(n)$ denote the number of "$1$"s in the dyadic representation of a
positive integer $n$ and sequence $S(n) = s(1)+s(2)+\dots+s(n-1)$.
The Trollope-Delange formula is a classic result that represents the
sequence $S$ in terms of the Takagi function. In this work, we replace
the usual sum of digits $s(n)$ with its weighted analogue and obtain a
variant of the Trollope-Delange formula for this case.
[Comments]
Russian, 7 pp.
Preprint is an updated variant of arXiv:1801.03120v3
[Contact e-mail]
aminabutdinov@gmail.com