| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
In note 209, Gilbert has found numbers that in one base are equal to their reverse in another base. This suggests a more general problem: Find the smallest number that can be written in 3 different bases and such that these 3 base representations are distinct permutations of one another (not including the identity permutation).
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 212.1 | MILOS::THIEL | Mon Jan 21 1985 22:40 | 12 | ||
The smallest such number with 3 digits is 11. In base 3, 11 is 102 In base 5, 11 is 021 In base 9, 11 is 012 11 is obviously also a solution for numbers with n digits, merely by prefixing zeroes. But is there a smaller value than 11 possible is more digits are present. I doubt it because the place values rise so fast. All of this, of course, assumes an integral positive radix. | |||||
| 212.2 | HARE::STAN | Tue Jan 22 1985 14:20 | 3 | ||
Good. But now let's see one with no leading zeroes, please. | |||||
| 212.3 | STAR::THIEL | Tue Jan 22 1985 20:19 | 7 | ||
With no leading zeroes, the minimal 3 digits answer is: Base 13: 2C1 = 495 Base 17: 1C2 = 495 Base 21: 12C = 495 where C is the digit (12) | |||||
| 212.4 | TOOLS::STAN | Sat Oct 19 1985 00:42 | 1 | ||
Is it possible if we only allow circular permutations? | |||||
| 212.5 | R2ME2::GILBERT | Sun Oct 20 1985 20:05 | 3 | ||
Base 25: 825 = 5055 Base 31: 582 = 5055 Base 49: 258 = 5055 | |||||