Sisyphus strings can be represented by several functions. We call it Sisyphus series, and the expression is as follows.

F is the first-order primitive function, and the k-order general term is its iteration period.

Its vba program code detailed bottom directory.

Set any number string and count the total number of even numbers, odd numbers and numbers contained in it.

For example: 568 124572 1, the even number is 5, the odd number is 5, and the total number is 10.

Discard the answers in the order of "parity total" and get a new number: 55 10.

Repeat the new number 55 10 according to the above rules to get the new number: 134.

Repeat the new number 134 according to the above rules to get a new number: 123.

Repeat the above rules for any number string, and finally you will get the result of "123". In other words, the final result of any number cannot escape from the 123 black hole. This is the mathematical black hole "Sisyphus string". Sisyphus's story comes from Greek mythology. God punished Sisyphus, king of Corinth, for pushing a boulder to the top of a steep hill, but no matter how hard he tried, the boulder inevitably rolled down at the top of the hill, so he had to push it again, endlessly. The number string "123" is called "Sisyphus string", which means that if any number string is repeated according to the above rules, the result is "123". Once it is transformed into "123", no matter how many times it is repeated according to the above rules, the transformed result will be repeated endlessly every time.

Why is there a mathematical black hole "Sisyphus string"?

(1) When it is a single digit, if it is odd, then k=0, n= 1, m= 1, which constitutes a new number 0 1 1, where k= 1, n.

If it is even, k= 1, n=0, m= 1, forming a new number10/,k= 1, n=2, m=3, and getting1.

(2) When it is a two-digit number, if it is odd and even, then k= 1, n= 1, m=2, forming a new number 1 12, then k= 1, n=2, m =

If it is two odd numbers, then k=0, n=2, m=2, and make up 022, then k=3, n=0, m=3, and get 303, then k= 1, n=2, m=3, and also get123;

If there are two even numbers, k=2, n=0, m = 2,202, k=3, n=0, m=3, 123 from the front.

(3) When it is a three-digit number, if the three-digit number consists of three even numbers, then k=3, n=0 and m=3, and 303 is obtained, then k= 1, n=2 and m=3, and123 is obtained;

If it is three odd numbers, k=0, n=3, m=3,033, k= 1, n=2, m = 3,123;

If it is parity, k=2, n= 1, m=3,213, k= 1, n=2, m = 3,123;

If it is even and odd, k= 1, n=2, m=3, you can get 123 immediately.

(4) when it is an m (m >; 3) Numbers, then this number consists of m numbers, including n odd numbers and k even numbers, m = n+k.

KNM connection generates a new number with fewer digits than the original number. Repeat the above steps, and you will definitely get a new three-digit knm.

The above is only the reason for this phenomenon. Simply analyze, if we take concrete mathematical proof, the steps of deductive reasoning are quite complicated and difficult. It was not until May of 20 10, 20 18 that the phenomenon of "Sisyphus string" was mathematically strictly proved by Qiu Ping, a Hui scholar in China, and was extended to six similar mathematical black holes ("123", "2 13" and "3/kloc-" This is his thesis: The Phenomenon of Sisyphus String (Mathematical Black Hole) and Its Proof (the text website is in the "Resources" at the bottom of this entry, you can click to read it). Since then, this puzzling mathematical mystery has been completely solved. Previously, Mr. Michel Ecker, a professor of mathematics at the University of Pennsylvania in the United States, only described this phenomenon, but failed to give a satisfactory answer and proof.