“吉祥数”的计数问题与杨辉三角

Counting Problem of "Auspicious Number" and Yang Hui Triangle

本文通过对"吉祥数"研究,发现各位"吉祥数"的个数数列与杨辉三角密切相关,并且正整数的各位"吉祥数"的个数数列是高阶等差数列,因此"吉祥数"问题可应用高阶等差数列的相关知识来解决.

Through the observation of ＂auspicious number＂,we find that the sequence of the number of ＂auspicious number＂ of each bit is closely related to Yang Hui triangle and the sequence of the number of ＂auspicious number＂ of each bit of positive integers is an arithmetic progression of higher order.Thus the problem about ＂auspicious number＂ can be solved using the related knowledge of arithmetic progression of higher order.