<?xml version="1.0" encoding="UTF-8" standalone="no"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> <title>fareylen</title> <link rel="stylesheet" type="text/css" href="csound.css" /> <link rel="stylesheet" type="text/css" href="syntax-highlighting.css" /> <meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /> <link rel="home" href="index.html" title="The Canonical Csound Reference Manual" /> <link rel="up" href="OpcodesTop.html" title="Orchestra Opcodes and Operators" /> <link rel="prev" href="faustgen.html" title="faustgen" /> <link rel="next" href="fareyleni.html" title="fareyleni" /> </head> <body> <div class="navheader"> <table width="100%" summary="Navigation header"> <tr> <th colspan="3" align="center">fareylen</th> </tr> <tr> <td width="20%" align="left"><a accesskey="p" href="faustgen.html">Prev</a> </td> <th width="60%" align="center">Orchestra Opcodes and Operators</th> <td width="20%" align="right"> <a accesskey="n" href="fareyleni.html">Next</a></td> </tr> </table> <hr /> </div> <div class="refentry"> <a id="fareylen"></a> <div class="titlepage"></div> <a id="IndexFareylen" class="indexterm"></a> <div class="refnamediv"> <h2> <span class="refentrytitle">fareylen</span> </h2> <p>fareylen — returns the length of a Farey Sequence. </p> </div> <div class="refsect1"> <a id="idm281472938262584"></a> <h2>Description</h2> <p> This opcode can be used in conjunction with <a class="link" href="GENfarey.html" title="GENfarey"><em class="citetitle">GENfarey</em></a>. It calculates the length of Farey Sequence F<sub>n</sub>. Its length is given by: |F<sub>n</sub>| = 1 + SUM over n phi(m) where phi(m) is Euler's totient function, which gives the number of integers ≤ m that are coprime to m. </p> <p> Some values for the length of F<sub>n</sub> given n: </p> <div class="informaltable"> <table class="informaltable" border="1"> <colgroup> <col /> <col /> </colgroup> <thead> <tr> <th>n</th> <th>F<sub>n</sub></th> </tr> </thead> <tbody> <tr> <td>1</td> <td>2</td> </tr> <tr> <td>2</td> <td>3</td> </tr> <tr> <td>3</td> <td>5</td> </tr> <tr> <td>4</td> <td>7</td> </tr> <tr> <td>5</td> <td>11</td> </tr> <tr> <td>6</td> <td>13</td> </tr> <tr> <td>7</td> <td>19</td> </tr> <tr> <td>8</td> <td>23</td> </tr> <tr> <td>9</td> <td>29</td> </tr> <tr> <td>10</td> <td>33</td> </tr> <tr> <td>11</td> <td>43</td> </tr> <tr> <td>12</td> <td>47</td> </tr> <tr> <td>13</td> <td>59</td> </tr> <tr> <td>14</td> <td>65</td> </tr> <tr> <td>15</td> <td>73</td> </tr> <tr> <td>16</td> <td>81</td> </tr> <tr> <td>17</td> <td>97</td> </tr> <tr> <td>18</td> <td>103</td> </tr> <tr> <td>19</td> <td>121</td> </tr> <tr> <td>20</td> <td>129</td> </tr> </tbody> </table> </div> <p> </p> </div> <div class="refsect1"> <a id="idm281472938188312"></a> <h2>Syntax</h2> <pre class="synopsis">kfl <span class="command"><strong>fareylen</strong></span> kfn</pre> </div> <div class="refsect1"> <a id="idm281472938186072"></a> <h2>Performance</h2> <p> The length of the identified Farey sequence is returned. </p> <p> <span class="emphasis"><em>kfn</em></span> -- Integer identifying the sequence. </p> </div> <div class="refsect1"> <a id="idm281472938183800"></a> <h2>Credits</h2> <p> </p> <table border="0" summary="Simple list" class="simplelist"> <tr> <td>Author: Georg Boenn </td> </tr> <tr> <td>University of Glamorgan, UK</td> </tr> </table> <p> </p> <p>New in Csound version 5.13</p> </div> </div> <div class="navfooter"> <hr /> <table width="100%" summary="Navigation footer"> <tr> <td width="40%" align="left"><a accesskey="p" href="faustgen.html">Prev</a> </td> <td width="20%" align="center"> <a accesskey="u" href="OpcodesTop.html">Up</a> </td> <td width="40%" align="right"> <a accesskey="n" href="fareyleni.html">Next</a></td> </tr> <tr> <td width="40%" align="left" valign="top">faustgen </td> <td width="20%" align="center"> <a accesskey="h" href="index.html">Home</a> </td> <td width="40%" align="right" valign="top"> fareyleni</td> </tr> </table> </div> </body> </html>