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 s...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.展开更多
回文数猜想是一个著名的数学问题,尤其是自然数196,至今尚未证实是否是Lychrel数。为了在32位计算机上实现检验回文数猜想的196算法,提出在VC++平台下用字符串来实现。给出了算法的具体形式,对程序中每一个步骤予以详细说明。最后实验...回文数猜想是一个著名的数学问题,尤其是自然数196,至今尚未证实是否是Lychrel数。为了在32位计算机上实现检验回文数猜想的196算法,提出在VC++平台下用字符串来实现。给出了算法的具体形式,对程序中每一个步骤予以详细说明。最后实验证实了算法突破了W indow s XP的32位字长限制。展开更多
文摘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.
