495 (number)

From Wikipedia, the free encyclopedia
Jump to: navigation, search
494 495 496
Cardinal four hundred and ninety-five
Ordinal 495th
(four hundred and ninety-fifth)
Factorization 32· 5 · 11
Roman numeral CDXCV
Binary 1111011112
Ternary 2001003
Quaternary 132334
Quinary 34405
Senary 21436
Octal 7578
Duodecimal 35312
Hexadecimal 1EF16
Vigesimal 14F20
Base 36 DR36

495 is the integer after 494 and before 496. It is a pentatope number (and so a binomial coefficient  \tbinom {12}4 ).

Kaprekar transformation[edit]

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[edit]

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 repdigits 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.

See also[edit]

  • Collatz conjecture — sequence of unarranged-digit numbers always ends with the number 1.

References[edit]

  • Eldridge, Klaus E.; Sagong, Seok (February 1988). "The Determination of Kaprekar Convergence and Loop Convergence of All Three-Digit Numbers". The American Mathematical Monthly (The American Mathematical Monthly, Vol. 95, No. 2) 95 (2): 105–112. doi:10.2307/2323062. JSTOR 2323062.