An integrality phenomenon

Florian Fürnsinn; Danylo Radchenko; Wadim Zudilin

An integrality phenomenon

Number Theory 2026-04-21 v2 Classical Analysis and ODEs Combinatorics

Authors: Florian Fürnsinn , Danylo Radchenko , Wadim Zudilin

Abstract

We prove a general statement about the integrality of the sequences generated by a recursion of the following form: $nu_n$ equals a linear combination of $u_{n-1},u_{n-2},\dots,u_0$ with polynomial coefficients in $n$ of special form. This includes a conjectural integrality of the sequence related to the H\"ormander-Bernhardsson extremal function, for which we further give a direct proof as well.

Keywords

integer sequences and recurrences collatz conjecture exponential sums

Cite

@article{arxiv.2603.25506,
  title  = {An integrality phenomenon},
  author = {Florian Fürnsinn and Danylo Radchenko and Wadim Zudilin},
  journal= {arXiv preprint arXiv:2603.25506},
  year   = {2026}
}

Comments

v2, 5 pages. Minor corrections

An integrality phenomenon

Abstract

Keywords

Cite

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