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ZENODO
Preprint . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
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Evaluation of GPT-5 on an Advanced Extension of Kashihara's Problem

Authors: Marco, Ripà; OpenAI ChatGPT;

Evaluation of GPT-5 on an Advanced Extension of Kashihara's Problem

Abstract

This work presents the solution of Problem 1 of Question #30 from Comments and Topics on Smarandache Notions and Problems, published in 1996 by Kenichiro Kashihara, corresponding to Problem 16 of Only Problems, Not Solutions!. It is a recreational mathematics problem that remained open until 2010, when an extended version was published in Appendix 2 of Divisibilità per 3 degli elementi di particolari sequenze numeriche, Rudi Mathematici Bookshelf. The question concerns OEIS sequence A001292 (the so-called "circular sequence") and the probability that a generic element ends with a given digit c∈{0,1,2,...,9}. In 2010, an enhanced version of the problem was studied, providing the general formula of this probability as a function of the length of the last complete block and of c, and using the exact value to bound the interval in which the probability lies in the inter-block (partial block) case, as reported in note 14 on page 17 of the aforementioned work. On August 9, 2025, GPT-5 independently solved the same enhanced version of Kashihara's question, proposing a more compact formula and extending it exactly to the incomplete block case as well.

Keywords

Artificial Intelligence/statistics & numerical data, Number theory, Recreational mathematics, Kashihara problem, GPT test, Artificial Intelligence/statistics & numerical data, Digit distribution, Probability, OEIS

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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