2
<refentry id="fareylen">
3
<indexterm id="IndexFareylen"><primary>fareylen</primary></indexterm>
4
<refentryinfo><title>Miscellaneous</title></refentryinfo>
6
<refentrytitle>fareylen</refentrytitle>
10
<refname>fareylen</refname>
12
returns the length of a Farey Sequence.
17
<title>Description</title>
19
This opcode can be used in conjunction with <link linkend="GENfarey"><citetitle>GENfarey</citetitle></link>.
20
It calculates the length of Farey Sequence F<subscript>n</subscript>. Its length is given by:
21
|F<subscript>n</subscript>| = 1 + SUM over n phi(m)
22
where phi(m) is Euler's totient function, which gives the number of integers ≤ m that are coprime to m.
25
Some values for the length of F<subscript>n</subscript> given n:
27
<listitem>n |F<subscript>n</subscript>|</listitem>
28
<listitem>1 2</listitem>
29
<listitem>2 3</listitem>
30
<listitem>3 5</listitem>
31
<listitem>4 7</listitem>
32
<listitem>5 11</listitem>
33
<listitem>6 13</listitem>
34
<listitem>7 19</listitem>
35
<listitem>8 23</listitem>
36
<listitem>9 29</listitem>
37
<listitem>10 33</listitem>
38
<listitem>11 43</listitem>
39
<listitem>12 47</listitem>
40
<listitem>13 59</listitem>
41
<listitem>14 65</listitem>
42
<listitem>15 73</listitem>
43
<listitem>16 81</listitem>
44
<listitem>17 97</listitem>
45
<listitem>18 103</listitem>
46
<listitem>19 121</listitem>
54
<synopsis>kfl <command>fareylen</command> kfn</synopsis>
58
<title>Performance</title>
60
The length of the identified Farey sequence is returned.
64
<emphasis>kfn</emphasis> -- Integer identifying the sequence.
69
<title>Credits</title>
72
<member>Author: Georg Boenn </member>
73
<member>University of Glamorgan, UK</member>
77
<para>New in Csound version 5.13</para>
added
removed
opcodes/fareylen.xml
