81–90 of 109 posts
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.
fpprintprec:100; fpprec:100; s : string(bfloat(1)/bfloat(9998)); makelist(substring(s,3+4i,7+4i),i,0,15); [0002, 0004, 0008, 0016, 0032, 0064, 0128, 0256, 0512, 1024, 2048,4096, 8193,broken pattern,6387, 2774, 5549]
Earlier quoted context omitted.
> 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.
Earlier quoted context omitted.
The pattern is not really breaking. What happens is that 16384 doesn't fit in a 4 digit space so it's first digit "1" jumps to 8192 and it becomes 8193. Then the next number (32768) add it's first digit "3" to 16384 and it becomes 16387 and so on, so the sequence appears strange after 4096: ...409681936387...
I think that's what you would call a break in a pattern though. Of course, the infinite series will stay infinite.
Powers of 3:
1/9997 = 0.0001 0003 0009 0027 0081 ...
Powers of 4:
1/9996 = 0.0001 0004 0016 0064 0256 ...
Powers of 5:
1/9995 = 0.0001 0005 0025 0125 0625 ...
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
56.96124843225 ^ 56.96124843225
Wolfram confirms that it's pretty close to a full googol. Of course, you can keep adding digits to the end of the number to make it even more precise. Maybe I'll write a script to do that.
Not related, but 12345679 * 8 = 98765432
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
On a vaguely similar, yet less practical note: 111,111,111 * 111,111,111 = 12,345,678,987,654,321 :)
It's also a useful self-test if you think the battery might be going.
fibonacci: 100000000/99989999=1.000100020003000500080013002100340055...
integers: 1000000/998001=1.002003004005006...
square numbers: 1001000000/997002999=1.004009016025036...
explanations and proofs at: http://www.joefkelley.com/?p=635