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1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..

wolframalpha.com

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Re: 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..

#42

Post by arbitrage »

kachnuv_ocasek wrote: post #35

I gotta be that guy: Why is this the first post on the front page of Hacker News? Is basic arithmetic really so fascinating to the computer people?

In fact, you do not have to be that guy. Different people find different things interesting; just let it go.

Re: 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..

#44

Post by rjbwork »

lelf wrote: post #21
crntaylor wrote: post #10

The pattern will break down once you get past 8192, which is 2^13. That means that the pattern continues for an impressive 52 significant figures (well, it actually breaks down on the 52nd digit, which will be a 3 instead of a 2). The reason it works is that 9998 = 10^4 - 2. You can expand as 1 / (10^n - 2) = 1/10^n * 1/(1 - 2/10^n) = 1/10^n * (1 + 2/10^n + 2^2 /10^2n + 2^3 /10^3n + ...) which gives the observed patt…

> The pattern will break down It doesn't actually: 4096 8193 6387 = 4096+8192 + 1 6384 + …

I noticed this on the last bit of wolframs display space also. The fact that it continues and is basically infinite sequence arithmetic overflow is insanely beautiful.

Re: 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..

#46

Post by geoffhotchkiss »

antimatter15 wrote: post #37

In high school, I was pretty fond of plugging 11^n to get rows of Pascal's triangle. It breaks down at row 5, but inserting 0's in the middle extends it (e.g. 101^n, 1001^n, 10001^n). 11^0 1 11^1 1 1 11^2 1 2 1 11^3 1 3 3 1 11^4 1 4 6 4 1

It actually doesn't break, you just have to do the carries as you would during normal addition. You have to read from right to left (1's place, 10's place, 100's place, and so on). So you're really just converting to base 10.

5th row: 1 5 10 10 5 1

Writing this a bit backwards, 1 * 1 + 5 * 10 + 10 * 100 + 10 * 1000 + 5 * 10000 + 1 * 100000 = 161051 = 11^5.

Re: 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..

#47

Post by pg_is_a_butt »

kachnuv_ocasek wrote: post #35

I gotta be that guy: Why is this the first post on the front page of Hacker News? Is basic arithmetic really so fascinating to the computer people?

looks like someone doesn't understand anything about number theory and how computer's actually work with number representations to make your stupid fucking twitterbook feed work. you're an idiot.

Re: 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..

#48

Post by pg_is_a_butt »

kachnuv_ocasek wrote: post #35

I gotta be that guy: Why is this the first post on the front page of Hacker News? Is basic arithmetic really so fascinating to the computer people?

looks like someone doesn't understand anything about number theory and how computers actually work with number representations to make your stupid fucking twitterbook feed work. you're an idiot.
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