495 (number)
| ||||
|---|---|---|---|---|
| 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 [math]\displaystyle{ \tbinom {12}4 }[/math]). The maximal number of pieces that can be obtained by cutting an annulus with 30 cuts.[2]
Kaprekar transformation
The Kaprekar's routine algorithm is defined as follows for three-digit numbers:
- Take any three-digit number, other than repdigits such as 111. Leading zeros are allowed.
- Arrange the digits in descending and then in ascending 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 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
- ↑ "Sloane's A000332". OEIS Foundation. https://oeis.org/A000332.
- ↑ Sloane, N. J. A., ed. "Sequence A000096". OEIS Foundation. https://oeis.org/A000096.
- 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.
fr:Nombres 400 à 499#495 ja:400#481 から 499
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