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Distribution of 0 digits in factorial series: Difference between revisions
Distribution of 0 digits in factorial series (view source)
Revision as of 17:02, 10 June 2021
, 2 years ago→{{header|REXX}}: added the computer programming language REXX.
m (→{{header|REXX}}: added a stub for REXX.) |
(→{{header|REXX}}: added the computer programming language REXX.) |
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=={{header|REXX}}==
<lang rexx>/*REXX program computes the mean of the proportion of "0" digits a series of factorials.*/
parse arg $ /*obtain optional arguments from the CL*/
if $='' | $="," then $= 100 1000 10000 /*not specified? Then use the default.*/
<pre>▼
#= words($) /*the number of ranges to be used here.*/
numeric digits 100 /*increase dec. digs, but only to 100. */
big= word($, #); != 1 /*obtain the largest number in ranges. */
do i=1 for big /*calculate biggest ! using 100 digs.*/
!= ! * i /*calculate the factorial of BIG. */
end /*i*/
if pos('E', !)>0 then do /*if its in exponential format, get EXP*/
parse var ! 'E' x /*parse the exponent from the number. */
numeric digits x+1 /*set the decimal digits to X plus 1.*/
end /* [↑] the +1 is for the dec. point.*/
title= ' mean proportion of zeros in the (decimal) factorial products for N'
say ' N │'center(title, 80) /*display the title for the output. */
say '───────────┼'center("" , 80, '─') /* " a sep " " " */
do j=1 for #; n= word($, j) /*calculate some factorial ranges. */
p= 0dist(n) /* " the proportion of zeros. */
say center( commas(n), 11)'│' left(p/n, 75)... /*display the results for above range. */
end /*j*/
say '───────────┴'center("" , 80, '─') /*display a foot sep for the output. */
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
/*──────────────────────────────────────────────────────────────────────────────────────*/
0dist: procedure; parse arg target; != 1; y= 0
do k=1 for target; != ! * k; z= countstr(0, !); y= y+ z/length(!)
end /*k*/
return y</lang>
{{out|output|text= when using the default inputs:}}
▲<pre>
N │ mean proportion of zeros in the (decimal) factorial products for N
───────────┼────────────────────────────────────────────────────────────────────────────────
100 │ 0.2467531861674322177784158871973526991129407033266153063813195937196095976...
1,000 │ 0.2035445511031646356400438031711455302985741167890402203486699704599684047...
10,000 │ 0.1730038482418660531800366428930706156810278809057883361518852958446868172...
───────────┴────────────────────────────────────────────────────────────────────────────────
</pre>
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