One of my favorite ways to waste time.
Using the tried and true method of looking up a result rather than
calculating it (of course it requires a sufficient set of information) -
iMi7-2:jstuff jkt$ cat pi.ijs
require 'jmf'
2 map_jmf_ 'pi';'/Users/jkt/Downloads/pi/y-cruncher v0.5.5.9187 (fix
2)/Pi - Dec - Chudnovsky.txt';'';1
where =: 3 : 'I. (": y) E. pi'
iMi7-2:jstuff jkt$ ja pi.ijs
NB. http://en.wikipedia.org/wiki/Feynman_point
(760 + i.12) { pi
134999999837
where 6666666666 NB. a beastly number...
386980413
(386980413 + 5 + i: 8) { pi
70566666666669143
102{. pi
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
$pi
500000002
I have amused myself by thinking about the probability of finding a
specific number within the random sequence of pi. For example, the
probability of any 10 digit sequence is fairly low. But one should
certainly find shorter sequences -
$where 123456789 NB. in the first 5e8 digits of pi
0
$where 12345678
3
$where 1234567
42
As I said, a favorite way to waste time.... One of these days I'll get
some more memory and calculate more digits (the 5e8 digits required 4
Gbytes of ram - which is reasonably modest when one thinks about it).
On 2015/01/06 13:23 , Roger Hui wrote:
Ah, in that case you can use the formula in the Wikipedia page you cited
<https://en.wikipedia.org/wiki/Approximations_of_%CF%80#Digit_extraction_methods>.
The first formula has the factor (%16)^n . That factor limits the
contribution to the n-th hex digit both from the left and from the right.
g=: 3 : '+/ 4 _2 _1 _1 % 1 4 5 6 + 8x * y'
10^.16
1.20412
1e4%1.2
8333.33
t=: g 8334
t
8335925201r2470518805025963211
0j_10 ": t
3.3741597854e_9
That is, for the 8334-th hex digit (approximately the 1e4-th decimal
digit), you probably don't need to look at many terms before the 8334-th
one, or any of the terms after it.
2}.0j100 ": +/ (16x&^ %~ g"0) i.50
1415926535897932384626433832795028841971693993751058209749445922466544481906209319125159482533123957
1}.":<.@o. 10^100x
1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
Alternatively, enter
f 1e4
and wait. :-)
On Tue, Jan 6, 2015 at 1:04 PM, 'Pascal Jasmin' via Programming <
[email protected]> wrote:
to be more specific, a function that gets the 10000th digit of pi?
----- Original Message -----
From: Roger Hui <[email protected]>
To: Programming forum <[email protected]>
Cc:
Sent: Tuesday, January 6, 2015 3:58 PM
Subject: Re: [Jprogramming] nth digit of pi
Answering the letter if not the spirit of your question:
f=: 3 : '10|<.@o. 10x^y'
f"0 i.5 20
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4
6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 1 9 7
1 6 9 3 9 9 3 7 5 1 0 5 8 2 0 9 7 4 9 4
4 5 9 2 3 0 7 8 1 6 4 0 6 2 8 6 2 0 8 9
9 8 6 2 8 0 3 4 8 2 5 3 4 2 1 1 7 0 6 7
On Tue, Jan 6, 2015 at 12:50 PM, 'Pascal Jasmin' via Programming <
[email protected]> wrote:
I don't really understand this well:
http://en.wikipedia.org/wiki/Approximations_of_%CF%80#Digit_extraction_methods
is there a J program for finding the y th digit of pi (any base is ok)
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