{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T05:43:10Z","timestamp":1762062190173,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,7]],"date-time":"2022-08-07T00:00:00Z","timestamp":1659830400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Kurepa\u2019s function and his hypothesis have been investigated by means of numerical simulation. Particular emphasis has been given to the conjecture on its distribution, that should be one of a random uniform distribution, which has been verified for large numbers. A convergence function for the two has been found.<\/jats:p>","DOI":"10.3390\/axioms11080388","type":"journal-article","created":{"date-parts":[[2022,8,7]],"date-time":"2022-08-07T21:03:50Z","timestamp":1659906230000},"page":"388","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On the Distribution of Kurepa\u2019s Function"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1645-2071","authenticated-orcid":false,"given":"Nicola","family":"Fabiano","sequence":"first","affiliation":[{"name":"\u201cVin\u010da\u201d Institute of Nuclear Sciences\u2014National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12\u201314, 11351 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4604-2065","authenticated-orcid":false,"given":"Milanka","family":"Garda\u0161evi\u0107-Filipovi\u0107","sequence":"additional","affiliation":[{"name":"School of Computing, Union University, 11000 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3057-9784","authenticated-orcid":false,"given":"Nikola","family":"Mirkov","sequence":"additional","affiliation":[{"name":"\u201cVin\u010da\u201d Institute of Nuclear Sciences\u2014National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12\u201314, 11351 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6206-3961","authenticated-orcid":false,"given":"Vesna","family":"Todor\u010devi\u0107","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Organizational Sciences, University of Belgrade, Jove Ili\u0107a 154, 11000 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8254-6688","authenticated-orcid":false,"given":"Stojan","family":"Radenovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,7]]},"reference":[{"key":"ref_1","first-page":"147","article-title":"On the left factorial function !N","volume":"1","author":"Kurepa","year":"1971","journal-title":"Math. Balk."},{"key":"ref_2","first-page":"105","article-title":"O faktorijelima kona\u010dnih i beskona\u010dnih brojeva","volume":"296","author":"Kurepa","year":"1953","journal-title":"Rad. Jugosl. Akad. Znan. Umjet."},{"key":"ref_3","first-page":"51","article-title":"Uber die Faktoriellen der endlichen und unendlichen Zahlen","volume":"4","author":"Kurepa","year":"1954","journal-title":"Ac. Sci. Yougosl. Cl. Math."},{"key":"ref_4","first-page":"7","article-title":"Factorials of cardinal numbers and trees","volume":"19","author":"Kurepa","year":"1964","journal-title":"Glasnik Mat. Fiz. Astr."},{"key":"ref_5","first-page":"297","article-title":"Left factorial function in complex domain","volume":"3","author":"Kurepa","year":"1973","journal-title":"Math. Balk."},{"key":"ref_6","first-page":"19","article-title":"On Kurepa\u2019s problems in number theory","volume":"57","author":"Mijajlovixcx","year":"1995","journal-title":"Publ. Inst. Math. Beogr."},{"key":"ref_7","unstructured":"Ivi\u0107, A., Mamuzi\u0107, Z., Mijajlovi\u0107, \u017d., and Todor\u010devi\u0107, S. (1996). Selected Papers of \u0110uro Kurepa, Matemati\u010dki Institut SANU. Available online: http:\/\/www.mi.sanu.ac.rs\/novi_sajt\/publications\/data\/ZarkoMijajlovicSelectedPapersOfDjuroKurepa.pdf."},{"key":"ref_8","unstructured":"Mijajlovi\u0107, \u017d. (2021). Fifty Years of Kurepa\u2019s !n Hypothesis, Acad\u00e9mie Serbe des Sciences et des Arts. Available online: http:\/\/elib.mi.sanu.ac.rs\/files\/journals\/bltn\/46\/bltnn46p169-181.pdf."},{"key":"ref_9","first-page":"1","article-title":"On some new observations on Kurepa\u2019s left factorial","volume":"4","author":"Fabiano","year":"2022","journal-title":"Math. Anal. Contemp. Appl."},{"key":"ref_10","unstructured":"Fabiano, N., Mirkov, N., Mitrovi\u0107, Z.D., and Radenovi\u0107, S. (2022). A discussion on two old standing number theory problems: Collatz hypothesis, together with its relation to Planck\u2019s black body radiation, and Kurepa\u2019s conjecture on left factorial function. Advances in Applied Analysis and Number Theory, Springer."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5802\/jtnb.432","article-title":"Nombres de Bell et somme de factorielles","volume":"16","author":"Barsky","year":"2004","journal-title":"J. Theor. Nr. Bordx."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"527","DOI":"10.5802\/jtnb.775","article-title":"Erratum a l\u2019article Nombres de Bell et somme de factorielles","volume":"23","author":"Barsky","year":"2011","journal-title":"J. Theor. Nr. Bordx."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3061","DOI":"10.1090\/mcom\/3098","article-title":"Searching for a counterexample to Kurepa\u2019s conjecture","volume":"85","year":"2016","journal-title":"Math. Comput."},{"key":"ref_14","unstructured":"The PARI Group (2022, June 23). PARI\/GP Version 2.13.4, Univ. Bordeaux. Available online: http:\/\/pari.math.u-bordeaux.fr\/."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/8\/388\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:05:20Z","timestamp":1760141120000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/8\/388"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,7]]},"references-count":14,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["axioms11080388"],"URL":"https:\/\/doi.org\/10.3390\/axioms11080388","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,8,7]]}}}