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...
This work was supported by the National Natu- ral Science Foundation of China (No.20173023 and No.90203012) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (No.20020730006).
On the basis of information theory and statistical methods, we use mutual information, n- tuple entropy and conditional entropy, combined with biological characteristics, to analyze the long range correlation and shor...