{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T05:04:30Z","timestamp":1750309470048,"version":"3.41.0"},"reference-count":14,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2024,9,1]],"date-time":"2024-09-01T00:00:00Z","timestamp":1725148800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:p>\n            We construct explicit formulas for sequences of general terms formed by concatenations of the first\n            <jats:italic>n<\/jats:italic>\n            + 1 terms of an arithmetic progression in a natural number base. We highlight the non-holonomic character of these sequences and present our implementation for the sequences A007908 and A000422 on https:\/\/oeis.org. The code is available at https:\/\/github.com\/T3gu1a\/Concatenations. These formulas are useful for efficient computations of asymptotic terms in these sequences. In the case of A007908, the formula may help investigating the long-standing search of primes among its terms.\n          <\/jats:p>","DOI":"10.1145\/3717582.3717594","type":"journal-article","created":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T20:41:51Z","timestamp":1739306511000},"page":"101-104","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Explicit Formulas for Concatenations of Terms of An Arithmetic Progression"],"prefix":"10.1145","volume":"58","author":[{"given":"Florian","family":"Luca","sequence":"first","affiliation":[{"name":"School of Maths, Wits University, Johannesburg, South Africa"}]},{"given":"Bertrand Teguia","family":"Tabuguia","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Oxford, UK"}]}],"member":"320","published-online":{"date-parts":[[2025,2,11]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1080\/00150517.2022.12427470"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00026-008-0333-6"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(95)00173-5"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.37236\/1894"},{"key":"e_1_2_1_5_1","first-page":"1","volume-title":"On some non-holonomic sequences. 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Annals of Mathematics pp. 480--508 (1933)"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073884.1073886"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/178365.178368"},{"key":"e_1_2_1_11_1","volume-title":"The online encyclopedia of integer sequences","author":"Sloane N.J.","year":"2003","unstructured":"Sloane, N.J., et al.: The online encyclopedia of integer sequences (2003), website: https:\/\/oeis.org"},{"key":"e_1_2_1_12_1","volume-title":"Not Solutions! http:\/\/fs.unm.edu\/OPNS.pdf","author":"Smarandache F.","year":"1993","unstructured":"Smarandache, F.: Only Problems, Not Solutions! http:\/\/fs.unm.edu\/OPNS.pdf (1993), online; accessed in May 2024"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2024.102328"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1134\/S0361768822020104"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3717582.3717594","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3717582.3717594","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:17:15Z","timestamp":1750295835000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3717582.3717594"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["10.1145\/3717582.3717594"],"URL":"https:\/\/doi.org\/10.1145\/3717582.3717594","relation":{},"ISSN":["1932-2232","1932-2240"],"issn-type":[{"type":"print","value":"1932-2232"},{"type":"electronic","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2024,9]]},"assertion":[{"value":"2025-02-11","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}