{"title":"由两个拟人数字连接而成的三波那契数。","authors":"Mahadi Ddamulira","doi":"10.1007/s13398-020-00933-0","DOIUrl":null,"url":null,"abstract":"<p><p>Let <math> <msub><mrow><mo>(</mo> <msub><mi>T</mi> <mi>n</mi></msub> <mo>)</mo></mrow> <mrow><mi>n</mi> <mo>≥</mo> <mn>0</mn></mrow> </msub> </math> be the sequence of Tribonacci numbers defined by <math> <mrow><msub><mi>T</mi> <mn>0</mn></msub> <mo>=</mo> <mn>0</mn></mrow> </math> , <math> <mrow><msub><mi>T</mi> <mn>1</mn></msub> <mo>=</mo> <msub><mi>T</mi> <mn>2</mn></msub> <mo>=</mo> <mn>1</mn></mrow> </math> , and <math> <mrow><msub><mi>T</mi> <mrow><mi>n</mi> <mo>+</mo> <mn>3</mn></mrow> </msub> <mo>=</mo> <msub><mi>T</mi> <mrow><mi>n</mi> <mo>+</mo> <mn>2</mn></mrow> </msub> <mo>+</mo> <msub><mi>T</mi> <mrow><mi>n</mi> <mo>+</mo> <mn>1</mn></mrow> </msub> <mo>+</mo> <msub><mi>T</mi> <mi>n</mi></msub> </mrow> </math> for all <math><mrow><mi>n</mi> <mo>≥</mo> <mn>0</mn></mrow> </math> . In this note, we use of lower bounds for linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction procedure to find all Tribonacci numbers that are concatenations of two repdigits.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s13398-020-00933-0","citationCount":"22","resultStr":"{\"title\":\"Tribonacci numbers that are concatenations of two repdigits.\",\"authors\":\"Mahadi Ddamulira\",\"doi\":\"10.1007/s13398-020-00933-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Let <math> <msub><mrow><mo>(</mo> <msub><mi>T</mi> <mi>n</mi></msub> <mo>)</mo></mrow> <mrow><mi>n</mi> <mo>≥</mo> <mn>0</mn></mrow> </msub> </math> be the sequence of Tribonacci numbers defined by <math> <mrow><msub><mi>T</mi> <mn>0</mn></msub> <mo>=</mo> <mn>0</mn></mrow> </math> , <math> <mrow><msub><mi>T</mi> <mn>1</mn></msub> <mo>=</mo> <msub><mi>T</mi> <mn>2</mn></msub> <mo>=</mo> <mn>1</mn></mrow> </math> , and <math> <mrow><msub><mi>T</mi> <mrow><mi>n</mi> <mo>+</mo> <mn>3</mn></mrow> </msub> <mo>=</mo> <msub><mi>T</mi> <mrow><mi>n</mi> <mo>+</mo> <mn>2</mn></mrow> </msub> <mo>+</mo> <msub><mi>T</mi> <mrow><mi>n</mi> <mo>+</mo> <mn>1</mn></mrow> </msub> <mo>+</mo> <msub><mi>T</mi> <mi>n</mi></msub> </mrow> </math> for all <math><mrow><mi>n</mi> <mo>≥</mo> <mn>0</mn></mrow> </math> . In this note, we use of lower bounds for linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction procedure to find all Tribonacci numbers that are concatenations of two repdigits.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s13398-020-00933-0\",\"citationCount\":\"22\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13398-020-00933-0\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2020/9/15 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13398-020-00933-0","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2020/9/15 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 22
摘要
让T (n) n≥0被T Tribonacci之序列数字:0 = 0,T = T = 2 = 1, T和T n + 3 = n + 2 + T T n + 1 + n的所有n≥0。在这篇文章中,我们用下舱的线条来线性使用对数的数字和面包师减少的程序来寻找所有的数字,这些数字是两个重复的结果。
Tribonacci numbers that are concatenations of two repdigits.
Let be the sequence of Tribonacci numbers defined by , , and for all . In this note, we use of lower bounds for linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction procedure to find all Tribonacci numbers that are concatenations of two repdigits.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.