Farey sequence: Difference between revisions
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</pre>
=={{header|Arturo}}==
<syntaxhighlight lang="arturo">farey: function [n][
f1: [0 1]
f2: @[1 n]
result: @["0/1" ~"1/|n|"]
while [1 < f2\1][
k: (n + f1\1) / f2\1
aux: f1
f1: f2
f2: @[
(f2\0 * k) - aux\0,
(f2\1 * k) - aux\1
]
'result ++ (to :string f2\0) ++ "/" ++ (to :string f2\1)
]
return result
]
loop 1..11 'i ->
print [pad (to :string i) ++ ":" 3 join.with:" " farey i]
print ""
print "Number of fractions in the Farey sequence:"
loop range.step: 100 100 1000 'r ->
print "F(" ++ (pad (to :string r) 4) ++ ") = " ++ (pad to :string size farey r 6)
</syntaxhighlight>
{{out}}
<pre> 1: 0/1 1/1
2: 0/1 1/2 1/1
3: 0/1 1/3 1/2 2/3 1/1
4: 0/1 1/4 1/3 1/2 2/3 3/4 1/1
5: 0/1 1/5 1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 1/1
6: 0/1 1/6 1/5 1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 5/6 1/1
7: 0/1 1/7 1/6 1/5 1/4 2/7 1/3 2/5 3/7 1/2 4/7 3/5 2/3 5/7 3/4 4/5 5/6 6/7 1/1
8: 0/1 1/8 1/7 1/6 1/5 1/4 2/7 1/3 3/8 2/5 3/7 1/2 4/7 3/5 5/8 2/3 5/7 3/4 4/5 5/6 6/7 7/8 1/1
9: 0/1 1/9 1/8 1/7 1/6 1/5 2/9 1/4 2/7 1/3 3/8 2/5 3/7 4/9 1/2 5/9 4/7 3/5 5/8 2/3 5/7 3/4 7/9 4/5 5/6 6/7 7/8 8/9 1/1
10: 0/1 1/10 1/9 1/8 1/7 1/6 1/5 2/9 1/4 2/7 3/10 1/3 3/8 2/5 3/7 4/9 1/2 5/9 4/7 3/5 5/8 2/3 7/10 5/7 3/4 7/9 4/5 5/6 6/7 7/8 8/9 9/10 1/1
11: 0/1 1/11 1/10 1/9 1/8 1/7 1/6 2/11 1/5 2/9 1/4 3/11 2/7 3/10 1/3 4/11 3/8 2/5 3/7 4/9 5/11 1/2 6/11 5/9 4/7 3/5 5/8 7/11 2/3 7/10 5/7 8/11 3/4 7/9 4/5 9/11 5/6 6/7 7/8 8/9 9/10 10/11 1/1
Number of fractions in the Farey sequence:
F( 100) = 3045
F( 200) = 12233
F( 300) = 27399
F( 400) = 48679
F( 500) = 76117
F( 600) = 109501
F( 700) = 149019
F( 800) = 194751
F( 900) = 246327
F(1000) = 304193</pre>
=={{header|AWK}}==
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