Lukas Spiegelhofer

activity

20152025

most citedNormality of the Thue--Morse sequence along Piatetski-Shapiro sequences, II

21 citations · 60 across the 22 of their papers we have counts for

collaborators

Showing 2017Show all

9 papers · 1 filter

math.NT2017★ 1 cited

Divisibility of binomial coefficients by powers of two

Lukas Spiegelhofer, Michael Wallner

For nonnegative integers $j$ and $n$ let $Θ (j, n)$ be the number of entries in the $n$ -th row of Pascal's triangle that are not divisible by $2^{j + 1}$ . In this paper we prove that t…

math.CO2017

Continuants, run lengths, and Barry's modified Pascal triangle

Jeffrey Shallit, Lukas Spiegelhofer

We show that the $n$ 'th diagonal sum of Barry's modified Pascal triangle can be described as the continuant of the run lengths of the binary representation of $n$ . We also obtain a…

math.NT2017

Discrepancy results for the Van der Corput sequence

Lukas Spiegelhofer

Let $d_{N} = N D_{N} (ω)$ be the discrepancy of the Van der Corput sequence in base $2$ . We improve on the known bounds for the number of indices $N$ such that $d_{N} \leq lo g N /100$ . Moreov…

math.NT2017★ 1 cited

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 $b$ is invariant under \emph{digit reversal} in base $3$ , that is,…

math.NT2017★ 9 cited

Normality of the Thue--Morse sequence along Piatetski-Shapiro sequences

Lukas Spiegelhofer

We prove that for $1 < c < 4/3$ the subsequence of the Thue--Morse sequence $t$ indexed by $⌊ n^{c} ⌋$ defines a normal sequence, that is, each finite sequence $(\vare…

math.NT2017

Piatetski-Shapiro sequences via Beatty sequences

Lukas Spiegelhofer

Integer sequences of the form $⌊ n^{c} ⌋$ , where $1 < c < 2$ , can be locally approximated by sequences of the form $⌊ n α + β ⌋$ in a very good way. Following this app…

math.CO2017

The Tu--Deng Conjecture holds almost surely

Lukas Spiegelhofer, Michael Wallner

The Tu--Deng Conjecture is concerned with the sum of digits $w (n)$ of $n$ in base~ $2$ (the Hamming weight of the binary expansion of $n$ ) and states the following: assume that $k$ …

math.NT2017

Möbius orthogonality for the Zeckendorf sum-of-digits function

Michael Drmota, Clemens Müllner, Lukas Spiegelhofer

We show that the (morphic) sequence $(- 1)^{s_{φ} (n)}$ is asymptotically orthogonal to all bounded multiplicative functions, where $s_{φ}$ denotes the Zeckendorf sum-of-digits function.…

math.NT2017★ 1 cited

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…