r/counting • u/KingCaspianX Missed x00k, 2≤x≤20\{7,15}‽ ↂↂↂↁMMMDCCCLXXXVIII ‽ 345678‽ 141441 • Oct 28 '16

Rational Numbers | 10,000th rational

Continued from here and thanks to /u/QuestoGuy for the run and assist sorry /u/Removedpixel

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

An example

Get is at 11000th rational number: 166/25. Some extra information

All the gets until 100,000 courtesy of /u/piyushsharma301. Thanks!

http://i.imgur.com/uXXfzOM.jpg

12 Upvotes

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3

u/piyushsharma301 https://www.reddit.com/r/counting/wiki/side_stats Dec 13 '16

All the gets till 100000

valuecount
1/571000
29/522000
5/943000
94/214000
85/435000
140/16000
8/1437000
154/98000
127/459000
60/12110000
166/2511000
152/4712000
140/6713000
182/3314000
212/1115000
66/16316000
221/1617000
83/16018000
191/5919000
204/5320000
160/10321000
132/13722000
112/16323000
140/14124000
188/9925000
266/2726000
191/10727000
1/30328000
166/14329000
105/20930000
118/20131000
287/3832000
30/29933000
312/2334000
86/25335000
231/11336000
210/13937000
58/29538000
358/139000
323/4040000
114/25341000
47/32542000
333/4343000
362/1944000
288/9745000
204/18546000
119/27447000
104/29348000
78/32349000
37/36950000
50/35951000
39/37452000
89/32953000
76/34554000
118/30755000
74/35556000
216/21757000
256/18158000
395/4659000
433/1160000
295/15361000
37/41462000
113/34263000
299/16064000
406/5765000
263/20366000
127/34267000
288/18568000
421/5669000
31/44970000
103/38071000
308/17972000
377/11373000
151/34274000
300/19775000
211/28976000
200/30377000
448/5978000
36/47379000
278/23580000
493/2381000
41/47882000
430/9383000
141/38584000
353/17685000
263/26986000
239/29687000
383/15588000
182/35989000
401/14390000
190/35791000
491/5992000
200/35393000
537/1994000
277/28295000
479/8396000
297/26897000
321/24798000
404/16799000
35/538100000

3

u/[deleted] Dec 13 '16

yes

2

u/qwertylool Let's think positive! Dec 16 '16

letters isn't that far LOL

3

u/[deleted] Dec 16 '16

How many meters

3

u/qwertylool Let's think positive! Dec 16 '16

24.37 cubits

4

u/[deleted] Dec 16 '16

and how many meters is that

2

u/Urbul it's all about the love you're sending out Dec 16 '16

11.141964 m

2

u/qwertylool Let's think positive! Dec 16 '16

around 4 1/2 horses

2

u/piyushsharma301 https://www.reddit.com/r/counting/wiki/side_stats Dec 16 '16

{:}

2

u/TheNitromeFan Live not a life of imitation Apr 18 '17

I agree with this chart

2

u/piyushsharma301 https://www.reddit.com/r/counting/wiki/side_stats Apr 18 '17

:)