- 495 (number)
495 is the integer after 494 and before 496. It is a
pentatope number .Kaprekar transformation
The Kaprekar transformation is defined as follows for three-digit numbers:
# Start with a three-digit number with at least two digits different.
# Arrange the digits in ascending and then in descending order to get two three-digit numbers, adding leading zeros if necessary.
# Subtract the smaller number from the bigger number.
# Go back to step 2.Repeating this process will always reach 495 in a few steps. Once 495 is reached, the process stops because 954 – 459 = 495.
Example
For example, choose 598:
:985 − 589 = 396:963 − 369 = 594:954 − 459 = 495
The only three-digit numbers for which this function does not work are
repdigit s such as 111, which give the answer 0 after a single iteration. All other three-digits numbers work if leading zeros are used to keep the number of digits at 3::211 – 112 = 099:990 – 099 = 891 (rather than 99 - 99 = 0):981 – 189 = 792:972 – 279 = 693:963 – 369 = 594:954 − 459 = 495
The number 6174 has the same property for the four-digit numbers.
ee also
*
Collatz conjecture — sequence of unarranged-digit numbers always ends with the number 1.References
*cite journal|last=Eldridge|first=Klaus E. |coauthors= Sagong, Seok|title=The Determination of Kaprekar Convergence and Loop Convergence of All Three-Digit Numbers |journal= The American Mathematical Monthly|volume=95|issue=2|year=1988|month=February|pages=105–112|doi=10.2307/2323062
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