In mathematics, there is a number called narcissistic number, also called self-generated number. The personality of narcissistic numbers lies in that for any n-bit narcissistic number, the sum of the n powers of its digits is exactly the number itself.
Obviously, 1, 2, 3, ..., 9 are narcissistic numbers; There is no narcissism number when n = 2; When n = 3, there are four narcissistic numbers:
153= 1^3+5^3+3^3
370=3^3+7^3+0^3
37 1=3^3+7^3+ 1^3
407=4^3+0^3+7^3
Because Armstrong was the first person to notice narcissistic numbers, according to the unwritten smelly rules in mathematics, the third name of narcissistic numbers is Armstrong numbers ~ which is embarrassing.
Nelson has given all narcissistic numbers of n = 4 ~ 1963 through a lot of research:
n=4: 1634 8208 9474
n=5:54747 92727 93084
n=6:548834
Don't say anything above n = 7.
There are also some mathematical black holes, such as self-replicating numbers, also called Capolli's constant, which were discovered and named by Indian scholar Capolli Ka in 1954. Capolli card constant is a strange number: a number composed of different numbers, arranged in descending order, subtracted from the former, and the difference is still composed of the same number. Self-replication is less than narcissism. Only one combination of 3-digit 4, 5 and 9 meets the requirements, specifically 495. There is only one combination of self-replication of 4-digit: 1, 6, 4, 7, specifically 174.
Take any three digits, arrange them in descending order, then subtract the number obtained in ascending order, and continue to subtract ascending order from the new number. If you repeat it, you will definitely fall into the black hole of 495.
If you want to know more carefully and in detail, I suggest you read the series of Interesting Mathematics edited by Zhang Jingzhong, an academician of China Academy of Sciences. The content of mathematical black holes is in the book Rubik's Cube and Others edited by Wu.
Except 0 and 1, only 153, 370, 37 1 and 407 (these four numbers are called "narcissus numbers") are equal to themselves. For example, to make 153 a black hole, we start with any positive integer divisible by 3. Find the cubes of its numbers respectively, add these cubes to form a new number, and repeat this process. Besides the number of daffodils, there are four roses (including1634,8208,9474) and five pentagrams (including 54748,92727,93084). When the number of numbers is more than five, such numbers are called "self".