495 (number)

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← 494 495 496 →
Cardinal four hundred ninety-five
Ordinal 495th
(four hundred ninety-fifth)
Factorization 32× 5 × 11
Greek numeral ΥϞΕ´
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 (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 ).

Kaprekar transformation[edit]

The Kaprekar's routine algorithm 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]

  1. ^ "Sloane's A000332". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-16. 
  • 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.