495 (number)

495 (four hundred [and] ninety-five) is the natural number following 494 and preceding 496. It is a pentatope number[1] (and so a binomial coefficient ). The maximal number of pieces that can be obtained by cutting an annulus with 30 cuts.[2]

← 494 495 496 →
Cardinalfour hundred ninety-five
Ordinal495th
(four hundred ninety-fifth)
Factorization32 × 5 × 11
Greek numeralΥϞΕ´
Roman numeralCDXCV
Binary1111011112
Ternary2001003
Senary21436
Octal7578
Duodecimal35312
Hexadecimal1EF16

Kaprekar transformation

The Kaprekar's routine algorithm is defined as follows for three-digit numbers:

  1. Take any three-digit number, other than repdigits such as 111. Leading zeros are allowed.
  2. Arrange the digits in descending and then in ascending 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 and repeat.

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 495:

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-digit 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, albeit has a much greater percentage of workable numbers.

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

References
  1. "Sloane's A000332". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-16.
  2. Sloane, N. J. A. (ed.). "Sequence A000096". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  • 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.
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