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 ).
| ||||
---|---|---|---|---|
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 | |||
Octal | 7578 | |||
Duodecimal | 35312 | |||
Hexadecimal | 1EF16 |
Kaprekar transformation
The Kaprekar's routine algorithm is defined as follows for three-digit numbers:
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-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.
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gollark: I've decided to just update caddy and see if that helps, since I am a bit overdue for switching to v2.
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See also
- Collatz conjecture — sequence of unarranged-digit numbers always ends with the number 1.
References
- "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.
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