奶牛数之和为好奇数

Curious numbers as sum of two Narayana’s cows numbers

本文旨在找到所有可以表示为两个奶牛数之和的好奇数。奶牛数列满足三阶递归关系:N_(n)=N_(n-1)+N_(n-3)(n≥3)及N_(0)=0、N_(1)=N_(2)=1。针对奶牛数之和为好奇数的问题,建立相应丢番图方程,将方程整理成不同形式,通过对数线性型求出各个未知量的一个较大的上界;再通过缩减方法,把各个未知量的较大上界缩减为一个可计算上界;最后,根据未知量的可计算上界,应用Mathematica得出所有可表示为两个奶牛数之和的好奇数。

This paper aims to identify all curious numbers that can be represented as the sum of two Narayana's cows numbers.Narayana’s cows sequence satisfies the third-order linear recurrence relation N_(n)=N_(n-1)+N_(n-3)(n≥3) and N_(0)=0、N_(1)=N_(2)=1.For the problem of the sum of Narayana’s cows numbers being a curious num-bers,a corresponding Diophantine equation is established.Different forms of the equation are arranged,and a larger upper bound for each unknown variable is obtained through linear forms in logarithms.Then,using the reduction method,the upper bound of each unknown variable is reduced to a computable upper bound.Final-ly,based on the computable upper bound of the unknown variables,Mathematica is used to find all curious numbers expressible as the sum of two Narayana's cows numbers.