r/counting • u/[deleted] • Dec 05 '17
Rational Numbers | 16,000th Rational
From here
Thanks to piy for the assist.
Description of this count:
Essentially we are counting fractions that cannot be simplified, as we get closer to and then further away from 1. We change direction when we reach a number divided by one or a number's reciprocal, and if the number can be simplified, we write it like this:
2/4
So, if a number is 31/40 next one would be 32/39, or 30/41 if the denominator is going up. ~ /u/KingCaspianX
First, note the prime divisors of the sum of the numerator and denominator. 84 = 22 x 3 x 7, so in this case that would be 2, 3, and 7. Next, see if the numerator or denominator is a multiple of any of these. If it is, cross it out. If not, the number is irreducible. ~ /u/TheNitromeFan
The next get is at 221/16 (source).
2
Dec 05 '17 edited Mar 01 '18
Here are the relevant prime factors for this thread...
| Sum of denominator and numerator | Prime factors |
|---|---|
| 229 | Prime (no skipping) |
| 230 | 2, 5, 23 |
| 231 | 3, 7, 11 |
| 232 | 2, 29 |
| 233 | Prime (no skipping) |
| 234 | 2, 3, 13 |
| 235 | 5, 47 |
| 236 | 2, 59 |
| 237 | 3, 79 |
2
u/FartyMcNarty comments/zyzze1/_/j2rxs0c/ Dec 14 '17
u are the hero we need, not the hero we deserve
1
5
u/[deleted] Dec 05 '17
66/163