Lychrel Numbers in Base 10: A Probabilistic Approach  

作　　者：Rostand S. Kuitché Rostand S. Kuitché(The Research Team in Algebra and Logic (ERAL), Yaound, Cameroon)

机构地区：[1]The Research Team in Algebra and Logic (ERAL), Yaound, Cameroon

出　　处：《Advances in Pure Mathematics》2024年第8期667-694,共28页理论数学进展（英文）

摘　　要：For decades, Lychrel numbers have been studied on many bases. Their existence has been proven in base 2, 11 or 17. This paper presents a probabilistic proof of the existence of Lychrel number in base 10 and provides some properties which enable a mathematical extraction of new Lychrel numbers from existing ones. This probabilistic approach has the advantage of being extendable to other bases. The results show that palindromes can also be Lychrel numbers.For decades, Lychrel numbers have been studied on many bases. Their existence has been proven in base 2, 11 or 17. This paper presents a probabilistic proof of the existence of Lychrel number in base 10 and provides some properties which enable a mathematical extraction of new Lychrel numbers from existing ones. This probabilistic approach has the advantage of being extendable to other bases. The results show that palindromes can also be Lychrel numbers.

关 键 词：Probabilistic Approach PALINDROMES Lychrel Numbers Iteration Function DIGITS 

分 类 号：O17[理学—数学]