Digital Black Hole

What do you know on the fifth page of the fifth-grade elementary school mathematics textbook of pep ?" We talked about the digital black hole 6174.
This digital black hole was discovered in 1949 by Indian mathematician capayica. There are many similar digital black holes. The black hole was originally a concept in astronomy, indicating a celestial body with a very strong gravitational field. any material or even light would never escape after being sucked in by it. The word used in mathematics, as mentioned in the article,The mathematical black hole refers to the situation in which a natural number falls into a loop after some mathematical operation."
Black Hole with four digits6174Similar,The digital black hole of three digits is 495..
For example, 987-789 = 198,981-189 = 792,972-279 = 693,963-369 = 594,954-459 = 495,954-459 = 495,......
Another example is 601-016 = 585,855-558 = 297,972-279 = 693,963-369 = 594,954-459 = 495,954-459 = 495 ,......
Next we will introduce several interesting digital black holes.
1. Digital Black Hole153
Any number that is a multiple of 3. Find the number on each digit of this numberCubeAnd, get a new number, and then find the cube and a new number on each digit of the new number, finally, it must fall into the digital black hole "153 ".
For example, 63 is used.
63 + 33 = 216 + 27 = 243, 23 + 43 + 33 = 8 + 64 + 27 = 99,93 + 93 = 729 + 729 = 1458, 13 + 43 + 53 + 83 = 1 + 64 + 125 + 512 = 702,

73 + 03 + 23 = 243 + 0 + 8 = 351,33 + 53 + 13 = 153, 13 + 53 + 33 = 153,......
For example, 219 is used.
23 + 13 + 93 = 8 + 1 + 729 = 343, 73 + 33 + 83 = 512 + 27 + 512 = 882,83 + 83 + 23 = 512 + + 8 =, 13 + 03 + 33 + 23 = 1 + 0 + 27 + 8 = 36,

33 + 63 = 27 + 216 = 243,23 + 43 + 33 = 8 + 64 + 27 = 99,93 + 93 = 729 + 729 = 1458,13 + 43 + 53 + 83 = 1 + 64 + 125 + 512 = 702,73 + 03 + 23 = 343 + 0 + 8 = 351,33 + 53 + 13 = 27 + 125 + 1 = 153,13 + 53 + 33 = 153, ......
Digital black hole 153 is also called "the number of the Bible" For more information, see the previous article "Fantastic Number of 153 ".
2. Digital black hole 123
Take any number and obtain the number of even numbers, the number of odd numbers, the sum of the two numbers (that is, the number of digits of this number ), use the obtained three numbers as numbers to form a three-digit number. Repeat the preceding three digits to get a new three-digit number. In this case, it is bound to fall into the digital black hole 123.
For example, take 31415926. There are three even numbers: 4, 2, and 6, and five odd numbers: 3, 1, 1, 5, and 9. The sum of the two numbers is 3 + 5 = 8, the new number composed of numbers "3", "5", and "8" is 358;
The even number of 358 has 8, and the odd number has 5 and 8. The two are 1 + 2 = 3, the new number composed of numbers "1", "2", and "3" is 123.
For example, 142857 is used. There are three even numbers: 4, 2, and 8, and three odd numbers: 1, 5, and 7. The sum of the two numbers is 3 + 3 = 6, the new number composed of numbers "3", "3", and "6" is 336;
The even number of 336 has 6, and the odd number has 3 and 3. the sum of the two is 1 + 2 = 3, the new number composed of numbers "1", "2", and "3" is 123.
3. Digital black hole 1 and 4
Take a non-zero natural number, obtain the sum of squares of the numbers on each digit, obtain a new number, then obtain the sum of squares of the numbers on each digit, and obtain a new number, in this case, either 1 appears at the end, and then 1 is always followed; or 4 is displayed, followed by a cycle of 4, 16, 37, 58, 89, 145, 42, and 20.
For example, take 365.
32 + 62 + 52 = 9 + 36 + 25 = 70, 72 + 02 = 49 + 0 = 49,42 + 92 = 16 + 81 = 97,92 + 72 = 81 + 49 = 130,12 + 32 + 02 = 1 + 9 + 0 = 10, 12 + 02 = 1 + 0 = 1, 12 = 1, ......
Another example is 89.
82 + 92 = 64 + 81 = 145, 12 + 42 + 52 = 1 + 16 + 25 = + 22 = 16 + 4 = 20, 22 + 02 = 4 + 0 = 16, 12 + 62 = 1 + 36 = 37,32 + 72 = 9 + 49 = 58,52 + 82 = 25 + 64 = 89,82 + 92 = 64 + 81 = 145,12 + 42 + 52 = 1 + 16 + 25 = + 22 = 16 + 4 = 20, 22 + 02 = 4 + 0 = 4, ......
Digital black hole is a mysterious and interesting phenomenon. Its discovery is contingent. Its calculation process is very simple and unquestionable, but its proof is very difficult, some have no results yet. This is precisely what makes mathematics attractive. Introducing the digital black hole as a teaching material of mathematics culture is of great benefit to improve students' interest in learning mathematics and fully understand mathematics.