495 is the integer after 494 and before 496

496 (number)

Four hundred [and] ninety-six is the natural number following four hundred [and] ninety-five and preceding four hundred [and] ninety-seven.-In mathematics:...

. It is a pentatope number

Pentatope number

A pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1 either from left to right or from right to left.The first few numbers of this kind are :...

.

Kaprekar transformation

The Kaprekar transformation is defined as follows for three-digit numbers:

1. Start with a three-digit number with at least two digits different.
2. Arrange the digits in ascending and then in descending order to get two three-digit numbers, adding leading zeros if necessary.
3. Subtract the smaller number from the bigger number.
4. 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 589:

985 − 589 = 396

963 − 369 = 594

954 − 459 = 495

The only three-digit numbers for which this function does not work are repdigit

Repdigit

In recreational mathematics, a repdigit is a natural number composed of repeated instances of the same digit, most often in the decimal numeral system....

s such as 111, which give the answer 0

0 (number)

0 is both a numberand the numerical digit used to represent that number in numerals.It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems...

 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

6174 (number)

6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is notable for the following property:#Take any four-digit number, using at least two different digits...

 has the same property for the four-digit numbers.

See also

• Collatz conjecture
  Collatz conjecture
  The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture , Kakutani's problem , the Thwaites conjecture , Hasse's algorithm The Collatz conjecture is a...
  
  — sequence of unarranged-digit numbers always ends with the number 1.