21 citations · 60 across the 22 of their papers we have counts for
7 papers · 2 filters
Divisibility of binomial coefficients by powers of two
Lukas Spiegelhofer, Michael Wallner
For nonnegative integers and let be the number of entries in the -th row of Pascal's triangle that are not divisible by . In this paper we prove that t…
Discrepancy results for the Van der Corput sequence
Lukas Spiegelhofer
Let be the discrepancy of the Van der Corput sequence in base . We improve on the known bounds for the number of indices such that . Moreov…
A digit reversal property for an analogue of Stern's sequence
Lukas Spiegelhofer
We consider a variant of Stern's diatomic sequence, studied recently by Northshield. We prove that this sequence is invariant under \emph{digit reversal} in base , that is,…
Normality of the Thue--Morse sequence along Piatetski-Shapiro sequences
Lukas Spiegelhofer
We prove that for the subsequence of the Thue--Morse sequence indexed by defines a normal sequence, that is, each finite sequence $(\vare…
Piatetski-Shapiro sequences via Beatty sequences
Lukas Spiegelhofer
Integer sequences of the form , where , can be locally approximated by sequences of the form in a very good way. Following this app…
Möbius orthogonality for the Zeckendorf sum-of-digits function
Michael Drmota, Clemens Müllner, Lukas Spiegelhofer
We show that the (morphic) sequence is asymptotically orthogonal to all bounded multiplicative functions, where denotes the Zeckendorf sum-of-digits function.…
Statistical distribution of the Stern sequence
Sandro Bettin, Sary Drappeau, Lukas Spiegelhofer
We prove that the Stern diatomic sequence is asymptotically distributed according to a normal law, on a logarithmic scale. This is obtained by studying complex moments, and the ana…