Counterexamples to a late-iterate ordering conjecture for generalized Hofstadter functions

For every k≥4, some input n satisfies Fₖ^(2k+1)(n)>Fₖ₊₁^(2k+2)(n). The proof constructs inverse iterates whose exact gap is k−3. The finite witness F₄⁹(132)=8>7=F₅¹⁰(132) gives the first instance. The result concerns infinitely many parameters, not infinitely many violating inputs for each fixed parameter.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-26
DOI
https://doi.org/10.5281/zenodo.23679311
Primary Topic
Mathematical Dynamics and Fractals
Type
preprint
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preprint

Counterexamples to a late-iterate ordering conjecture for generalized Hofstadter functions

Dev D. Goyal
Zenodo (CERN European Organization for Nuclear Research)
Mathematical Dynamics and Fractals
preprint

Counterexamples to a late-iterate ordering conjecture for generalized Hofstadter functions

Dev D. Goyal
preprint en

Abstract

For every k≥4, some input n satisfies Fₖ^(2k+1)(n)>Fₖ₊₁^(2k+2)(n). The proof constructs inverse iterates whose exact gap is k−3. The finite witness F₄⁹(132)=8>7=F₅¹⁰(132) gives the first instance. The result concerns infinitely many parameters, not infinitely many violating inputs for each fixed parameter.

Zenodo (CERN European Organization for Nuclear Research)
Mathematical Dynamics and Fractals
DOIOpen Access PDFOpenAlex
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Counterexamples to a late-iterate ordering conjecture for generalized Hofstadter functions — Dev D. Goyal · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS