请输入您要查询的字词:

 

单词 KaprekarConstant
释义

Kaprekar constant


The Kaprekar constant Kk in a given base b is a k-digit number K such that subjecting any other k-digit number n (except the repunitMathworldPlanetmath Rk and numbers with k-1 repeated digits) to the following process:

1. Arrange the digits of n in ascending orderPlanetmathPlanetmath, forming the k-digit number a, and then in descending order, forming the k-digit number b.

2. If a>b, calculate a-b=c; otherwise b-a=c.

3. Goto step 1 using c instead of n.

eventuallyMathworldPlanetmath gives K. (This process is sometimes called the Kaprekar routine).

For b=10, the Kaprekar constant for k=4 is 6174. Using n=1729, we find that 9721 - 1279 gives 8442. Then 8442 - 2448 = 5994. Then 9954 - 4599 gives 5355. Then 5553 - 3555 gives 1998. Then 9981 - 1899 gives 8082. Then 8820 - 288 gives 8532. Then 8532 - 2538 finally gives 6174. (Some numbers take longer than others). K2 and K7 don’t exist for b=10.

随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 8:16:24