作为两个Repdigits和的Padovan数

IF 0.3 4区综合性期刊 Q4 MULTIDISCIPLINARY SCIENCES Comptes Rendus De L Academie Bulgare Des Sciences Pub Date : 2023-10-01 DOI:10.7546/crabs.2023.09.02

Merve Duman, Refik Keskin, Leman Hocaoğlu

{"title":"作为两个Repdigits和的Padovan数","authors":"Merve Duman, Refik Keskin, Leman Hocaoğlu","doi":"10.7546/crabs.2023.09.02","DOIUrl":null,"url":null,"abstract":"Padovan sequence $$(P_{n})$$ is given by $$P_{n}=P_{n-2}+P_{n-3}$$ for $$n\\geq3$$ with initial condition $$(P_{0},P_{1},P_{2})=(1,1,1)$$. A positive integer is called a repdigit if all of its digits are equal. In this study, we examine the terms of the Padovan sequence, which are the sum of two repdigits. It is shown that the largest term of the Padovan sequence which can be written as a sum of two repdigits is $$P_{18}=114=111+3.$$","PeriodicalId":50652,"journal":{"name":"Comptes Rendus De L Academie Bulgare Des Sciences","volume":"7 1","pages":"0"},"PeriodicalIF":0.3000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Padovan Numbers as Sum of Two Repdigits\",\"authors\":\"Merve Duman, Refik Keskin, Leman Hocaoğlu\",\"doi\":\"10.7546/crabs.2023.09.02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Padovan sequence $$(P_{n})$$ is given by $$P_{n}=P_{n-2}+P_{n-3}$$ for $$n\\\\geq3$$ with initial condition $$(P_{0},P_{1},P_{2})=(1,1,1)$$. A positive integer is called a repdigit if all of its digits are equal. In this study, we examine the terms of the Padovan sequence, which are the sum of two repdigits. It is shown that the largest term of the Padovan sequence which can be written as a sum of two repdigits is $$P_{18}=114=111+3.$$\",\"PeriodicalId\":50652,\"journal\":{\"name\":\"Comptes Rendus De L Academie Bulgare Des Sciences\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus De L Academie Bulgare Des Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7546/crabs.2023.09.02\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus De L Academie Bulgare Des Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7546/crabs.2023.09.02","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}

引用次数: 0

摘要

对于$$n\geq3$$，初始条件为$$(P_{0},P_{1},P_{2})=(1,1,1)$$, Padovan序列$$(P_{n})$$由$$P_{n}=P_{n-2}+P_{n-3}$$给出。如果一个正整数的所有数字都相等，那么这个正整数就被称为repdigit。在本研究中，我们研究了Padovan序列的项，它是两个repdigits的和。证明了可以写成两个数字和的Padovan序列的最大项是 $$P_{18}=114=111+3.$$

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Padovan Numbers as Sum of Two Repdigits

Padovan sequence $$(P_{n})$$ is given by $$P_{n}=P_{n-2}+P_{n-3}$$ for $$n\geq3$$ with initial condition $$(P_{0},P_{1},P_{2})=(1,1,1)$$. A positive integer is called a repdigit if all of its digits are equal. In this study, we examine the terms of the Padovan sequence, which are the sum of two repdigits. It is shown that the largest term of the Padovan sequence which can be written as a sum of two repdigits is $$P_{18}=114=111+3.$$

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Comptes Rendus De L Academie Bulgare Des Sciences 综合性期刊-综合性期刊

CiteScore

0.60

自引率

33.30%

发文量

181

审稿时长

3-6 weeks

期刊介绍： Founded in 1948 by academician Georgy Nadjakov, "Comptes rendus de l’Académie bulgare des Sciences" is also known as "Доклади на БАН","Доклады Болгарской академии наук" and "Proceeding of the Bulgarian Academy of Sciences". If applicable, the name of the journal should be abbreviated as follows: C. R. Acad. Bulg. Sci. (according to ISO)