{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/an-explicit-formula-generating-the-non","title":"An explicit formula generating the non-Fibonacci numbers","arxiv_id":"1105.1127","date":"2011-05-05","proceeding":null,"authors":["Bakir Farhi"],"abstract":"We show among others that the formula: $$ \\lfloor n + \\log_{\\Phi}\\{\\sqrt{5}(\\log_{\\Phi}(\\sqrt{5}n) + n) -5 + \\frac{3}{n}\\} - 2 \\rfloor (n \\geq 2), $$ (where $\\Phi$ denotes the golden ratio and $\\lfloor \\rfloor$ denotes the integer part) generates the non-Fibonacci numbers.","url_abs":"https://arxiv.org/abs/1105.1127v2","url_pdf":"https://arxiv.org/pdf/1105.1127v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"an-explicit-formula-generating-the-non","repo_url":"https://github.com/stdlib-js/math-base-special-nonfibonacci","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"an-explicit-formula-generating-the-non","repo_url":"https://github.com/stdlib-js/math-iter-sequences-nonfibonacci","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}