Beefy Boxes and Bandwidth Generously Provided by pair Networks
No such thing as a small change
 
PerlMonks  

Comment on

( #3333=superdoc: print w/ replies, xml ) Need Help??

Oh wow, so it is. Sorry, I didn't look at your code since you didn't mention that you had gone outside the parameters provided so I didn't think that you had done what I was doing.

In penance, here is a script that shows the repeat length for 1/$n only when that length isn't "boring". If $n is prime a repeat length of $n-1 is "boring". If $n is composite, the boring length is the max repeat length of its prime factors.

#!/usr/bin/perl -w use strict; Main(); exit(); sub repDig { my( $den, $num )= @_; $num ||= 1; my $rem= $num % $den; my %seen; my $rep= ''; while( 1 ) { $rem *= 10; last if exists $seen{$rem}; $seen{$rem}= length( $rep ); $rep .= int( $rem / $den ); $rem %= $den; } substr( $rep, 0, $seen{$rem} )= ''; return $rep; } sub factor { my( $r )= @_; my $f= ''; my @f; my $p= 2; while( 1 < $r ) { my $q= int( $r / $p ); last if $q < $p; my $e= 0; while( $r == $q*$p && $q ) { $e++; $r= $q; $q= int( $r / $p ); } if( $e ) { push @f, $p; $f .= "*$p"; $f .= "^$e" if 1 < $e; } $p += 2==$p ? 1 : 2; } if( 1 < $r || ! @f ) { push @f, $r; $f .= "*$r"; } substr( $f, 0, 1 )= ''; return $f, @f; } sub Main { my $dem= 1; my %r; while( 1 ) { my( $f, @f )= factor( ++$dem ); my $r= repDig( $dem ); $r= $r ? length($r) : 0; if( $f eq $dem ) { $r{$dem}= $r; next if $r == $dem-1; } else { my $max= 0; for( @f ) { $max= $r{$_} if $max < $r{$_}; } next if $r == $max; } printf "%8d: 1/%s\n", $r, $f; } }

and the first few lines of output:

0: 1/2 1: 1/3 0: 1/5 2: 1/11 6: 1/13 3: 1/3^3 15: 1/31 3: 1/37 5: 1/41 21: 1/43 42: 1/7^2 13: 1/53 3: 1/2*3^3 33: 1/67 35: 1/71 8: 1/73 13: 1/79 9: 1/3^4 41: 1/83 44: 1/89 42: 1/2*7^2 4: 1/101 34: 1/103 53: 1/107 3: 1/2^2*3^3 48: 1/7*17 22: 1/11^2 42: 1/127 3: 1/3^3*5 8: 1/137 46: 1/139 42: 1/3*7^2 75: 1/151 78: 1/157 66: 1/7*23 9: 1/2*3^4 81: 1/163 78: 1/13^2 43: 1/173 95: 1/191 42: 1/2^2*7^2 98: 1/197 99: 1/199 84: 1/7*29 30: 1/211 3: 1/2^3*3^3 30: 1/7*31 48: 1/13*17 113: 1/227 48: 1/2*7*17 7: 1/239 30: 1/241 22: 1/2*11^2 27: 1/3^5 42: 1/5*7^2 50: 1/251 3: 1/2*3^3*5 5: 1/271 69: 1/277 28: 1/281 141: 1/283 30: 1/7*41 272: 1/17^2 146: 1/293 42: 1/2*3*7^2 6: 1/3^3*11 66: 1/13*23 42: 1/7*43 153: 1/307 155: 1/311 79: 1/317 66: 1/2*7*23 144: 1/17*19 9: 1/2^2*3^4 138: 1/7*47 110: 1/331 78: 1/2*13^2 30: 1/11*31 294: 1/7^3 173: 1/347 116: 1/349 32: 1/353 48: 1/3*7*17 179: 1/359 342: 1/19^2 22: 1/3*11^2 78: 1/7*53 186: 1/373 84: 1/13*29 176: 1/17*23 42: 1/2^3*7^2 99: 1/397 200: 1/401 30: 1/13*31 9: 1/3^4*5 84: 1/2*7*29 6: 1/11*37 204: 1/409 174: 1/7*59 140: 1/421 215: 1/431 3: 1/2^4*3^3 30: 1/2*7*31 198: 1/19*23 219: 1/439 42: 1/3^2*7^2 48: 1/2*13*17 221: 1/443 32: 1/449 10: 1/11*41 152: 1/457 48: 1/3^3*17 154: 1/463 233: 1/467 66: 1/7*67 42: 1/11*43 48: 1/2^2*7*17 239: 1/479 66: 1/3*7*23 22: 1/2^2*11^2 27: 1/2*3^5 42: 1/2*5*7^2 112: 1/17*29 210: 1/7*71 78: 1/3*13^2 24: 1/7*73 52: 1/521 261: 1/523 240: 1/17*31

My favotite is: 42: 1/7^2

Now demonstrate your understanding by correctly predicting a number with a repeat length of 11 or 25.

- tye        


In reply to Re^3: Recurring Cycle of Fractions (same) by tye
in thread Recurring Cycle of Fractions by Limbic~Region

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post; it's "PerlMonks-approved HTML":



  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.
  • Log In?
    Username:
    Password:

    What's my password?
    Create A New User
    Chatterbox?
    and the web crawler heard nothing...

    How do I use this? | Other CB clients
    Other Users?
    Others avoiding work at the Monastery: (4)
    As of 2015-07-29 04:21 GMT
    Sections?
    Information?
    Find Nodes?
    Leftovers?
      Voting Booth?

      The top three priorities of my open tasks are (in descending order of likelihood to be worked on) ...









      Results (260 votes), past polls