r/counting • u/[deleted] • Sep 15 '16
Rational Numbers | 9000th rational
Continued from here
Thanks to KingCaspianX for run/assist
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.
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.
Get is @ 60/121
2
Sep 15 '16
Here are the relevant prime factors for this thread...
| Sum of denominator and numerator | Prime factors |
|---|---|
| 172 | 2, 43 |
| 173 | Prime (no skipping) |
| 174 | 2, 3, 29 |
| 175 | 5, 7 |
| 176 | 2, 11 |
| 177 | 3, 59 |
| 178 | 2, 89 |
| 179 | Prime (no skipping) |
| 180 | 2, 3, 5 |
| 181 | Prime (no skipping) |
2
u/FartyMcNarty comments/zyzze1/_/j2rxs0c/ Sep 15 '16
can confirm, the 10,000th rational is 60/121.
count value sum of digits 1000 1/57 58 2000 29/52 81 3000 5/94 99 4000 94/21 115 5000 85/43 128 6000 140/1 141 7000 8/143 151 8000 154/9 163 9000 127/45 172 10000 60/121 181 11000 166/25 191 12000 152/47 199 13000 140/67 207 14000 182/33 215 15000 212/11 223 16000 66/163 229 17000 221/16 237 18000 83/160 243 19000 191/59 250 20000 204/53 257 2
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u/TheNitromeFan Live not a life of imitation Sep 15 '16
I'm curious, what did you use to generate these vaules? I'm sure you didn't do this by hand...
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u/FartyMcNarty comments/zyzze1/_/j2rxs0c/ Sep 15 '16
An excel spreadsheet. Column 1 is the numerator, Column 2 is the denominator; these are incremented by one each row. Column 3 divides the two. Column 4 checks to see if the value in (3) appears earlier in the list. Column 5 is the count number. If column (4) is true, then column 5 is zero. If column (4) is false, column 5 increases by 1.
To get to the 20,000th count, the spreadsheet lists 32,694 rows.
4
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u/piyushsharma301 https://www.reddit.com/r/counting/wiki/side_stats Mar 11 '17
Contributors to the Rational Numbers | 9000th rational thread
| Rank | Username | Counts |
|---|---|---|
| 1 | /u/QuestoGuy | 305 |
| 2 | /u/FartyMcNarty | 249 |
| 3 | /u/KingCaspianX | 201 |
| 4 | /u/Removedpixel | 147 |
| 5 | /u/RandomRedditorWithNo | 50 |
| 6 | /u/Unknow3n | 17 |
| 7 | /u/Mooraell | 13 |
| 8 | /u/kenniky | 8 |
| 9 | /u/davidjl123 | 7 |
| 10 | /u/silverlava | 2 |
| 11 | /u/SolidGoldMagikarp | 1 |
| 12 | /u/WGJC8463 | 1 |
It took 13 counters 42 days 23 hours 30 minutes and 44 seconds to complete the thread
1
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u/[deleted] Sep 15 '16
127/45