关于_毕业论文

摘要正如天文学中存在着天体的黑洞，数学上也存在数的“黑洞”。数的“黑洞”是指某些整数，通过施加某种特定的运算，经过有限次迭代后，其结果进入一个循环怪圈的情况。而这种“特定的运算”即所谓的数学“变换”，因此，研究黑洞数问题实际上就是研究变换数列的黑洞数问题，该问题已经引起了国内外数学爱好者的广泛关注。本文首先对西西弗斯黑洞数、卡普雷卡尔黑洞数与水仙花黑洞数这三类常见的黑洞数及其性质进行归纳总结，然后构造了一个新的变换来研究黑洞数问题。一方面，通过归纳和总结已知的黑洞数的相关性质，我们可以发现黑洞数的相关特征，进而寻找黑洞数。如在归纳卡普雷卡尔黑洞数的性质时，我发现二位黑洞数只须从能被 9 整除的整数寻找，三位黑洞数只须从能被 99 整除的整数寻

找等重要特征。另一方面，我根据 0 到 9 这 10 个自然数是否是 3 的倍数，构造一个D变换，研究D变换下的黑洞数问题。我发现D变换有且只有三组黑洞数，分别是*40+、*170+、

*280, 248,288, 488,520, 78,408+。我们的结果说明：根据自然数的特征恰当地构造变换，88506

可以得到更多有趣的黑洞数，不断丰富黑洞数大家庭。

毕业论文关键词：黑洞数；西西弗斯黑洞数；卡普雷卡尔黑洞数；水仙花黑洞数； D变换

Abstract As there is an astronomical black hole in astronomy, there exits black hole of number in math。 It refers to that by using a specific operation, the results of some integers will enter a cycle in the process of iteration。 The "specific operation" is the so-called "transformation" in math。 So, studying the problem of black- hole number is actually studying the transformation sequence, and it has caused wide concern among the domestic and foreign mathematics lovers。 The passage studys the black-hole number by means of inducing the nature of Sisyphus black-hole number, Kaprekar constant, Narcissistic number, the three common black- hole number and constructing new transformation。 On the one hand, through inducing the nature of known black-hole numbers we can find their relevant characteristics to seek them。 For example, when summing up the nature of Kaprekar constant, I discover that two digit black-hole numbers just search from the integer pided by nine, three digit numbers search from the integer pided by ninety-nine and so on。 On the other hand, according to whether ten natural numbers about zero to nine can be pided by three, I construct D transformation, study it, and discover the D transformation has three

groups of black-hole number。 They are *40+、*170+、*280,248,288,488,520,78,408+。

Our results illustrate that constructing proper transformation on the basis of

characteristics natural numbers can gain more interesting numbers and enrich the big family of black-hole number。

Keyword: Sisyphus black-hole number； Kaprekar constant；

Narcissistic number； D transformation

摘要 i

Abstract ii

引言 1

1、黑洞数的概念及西西弗斯黑洞数 1

1。1 黑洞数的定义 1

1。2 西西弗斯黑洞数 1

2、卡普雷卡尔黑洞数关于:http://www.youerw.com/shuxue/lunwen_162265.html