Arithmetic dynamics | Mathematical constants

6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is renowned for the following rule: 1. * Take any four-digit number, using at least two different digits (leading zeros are allowed). 2. * Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary. 3. * Subtract the smaller number from the bigger number. 4. * Go back to step 2 and repeat. The above process, known as Kaprekar's routine, will always reach its fixed point, 6174, in at most 7 iterations. Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174. For example, choose 1495: 9541 – 1459 = 80828820 – 0288 = 85328532 – 2358 = 61747641 – 1467 = 6174 The only four-digit numbers for which Kaprekar's routine does not reach 6174 are repdigits such as 1111, which give the result 0000 after a single iteration. All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4. For numbers with three identical numbers and a fourth number that is one number higher or lower (such as 2111), it is essential to treat 3-digit numbers with a leading zero; for example: 2111 – 1112 = 0999; 9990 – 999 = 8991; 9981 – 1899 = 8082; 8820 – 288 = 8532; 8532 – 2358 = 6174. (Wikipedia).

From playlist everything

Magic number 6174 and Kaprekar's Operation on 4-digit Integers

#shorts #mathonshorts check out information on Kaprekar's operation from the wiki page: https://en.wikipedia.org/wiki/Kaprekar%27s_routine All 4-digit numbers will go to 6174 after a few steps of Kaprekar's operation.

From playlist Elementary Number Theory

This video was made for #MegaFavNumbers The sequence that is generated by cycles of bits and somehow related to prime numbers and multiplicative order of 2 mod 2n+1 Sequence: 3, 6, 15, 12, 255, 30, 63, 24, 315, 510, 33825, 60, 159783, 126, 255, 48, 65535, 630, 14942265, 1020, 4095, 67650

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From playlist Shorts

Kaprekar’s Constant: A Mathematical Curiosity #shorts

Check out my main channel @polymathematic! Kaprekar's Constant is actually a family of constants that recur over and over again given a certain number of digits to start with. The process works as described: begin with some four-digit number. Then re-arrange the digits in both ascending

From playlist polymathematic #shorts

6174 is also known as Kaprekar's Constant. More links & stuff in full description below ↓↓↓ This video features University of Nottingham physics professor Roger Bowley, who is also featured on our Sixty Symbols channel at http://www.youtube.com/sixtysymbols NUMBERPHILE Website: http://ww

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Pick any four digit whole number and you can follow this process to reach and stick at 6174

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