{"title":"广义卢卡斯序列中的梅森数","authors":"Alaa Altassan, Murat Alan","doi":"10.7546/crabs.2024.01.01","DOIUrl":null,"url":null,"abstract":"Let $$k \\geq 2$$ be an integer and let $$(L_{n}^{(k)})_{n \\geq 2-k}$$ be the $$k$$-generalized Lucas sequence with certain initial $$k$$ terms and each term afterward is the sum of the $$k$$ preceding terms. Mersenne numbers are the numbers of the form $$2^a-1$$, where $$a$$ is any positive integer. The aim of this paper is to determine all Mersenne numbers which lie inside $$k$$-Lucas sequences.","PeriodicalId":104760,"journal":{"name":"Proceedings of the Bulgarian Academy of Sciences","volume":"30 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mersenne Numbers in Generalized Lucas Sequences\",\"authors\":\"Alaa Altassan, Murat Alan\",\"doi\":\"10.7546/crabs.2024.01.01\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $$k \\\\geq 2$$ be an integer and let $$(L_{n}^{(k)})_{n \\\\geq 2-k}$$ be the $$k$$-generalized Lucas sequence with certain initial $$k$$ terms and each term afterward is the sum of the $$k$$ preceding terms. Mersenne numbers are the numbers of the form $$2^a-1$$, where $$a$$ is any positive integer. The aim of this paper is to determine all Mersenne numbers which lie inside $$k$$-Lucas sequences.\",\"PeriodicalId\":104760,\"journal\":{\"name\":\"Proceedings of the Bulgarian Academy of Sciences\",\"volume\":\"30 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Bulgarian Academy of Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7546/crabs.2024.01.01\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Bulgarian Academy of Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7546/crabs.2024.01.01","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let $$k \geq 2$$ be an integer and let $$(L_{n}^{(k)})_{n \geq 2-k}$$ be the $$k$$-generalized Lucas sequence with certain initial $$k$$ terms and each term afterward is the sum of the $$k$$ preceding terms. Mersenne numbers are the numbers of the form $$2^a-1$$, where $$a$$ is any positive integer. The aim of this paper is to determine all Mersenne numbers which lie inside $$k$$-Lucas sequences.
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