Farey sequence: Difference between revisions
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F900: 246327 members
F1000: 304193 members</pre>
=={{header|jq}}==
{{works with|jq}}
'''Also works with gojq, the Go implementation of jq, and with fq.'''
This solution uses two jq functions from the [[Arithmetic/Rational#jq]] page,
and can be included using jq's `include` directive.
<syntaxhighlight lang=jq>
include "rational" ; # actually, only `r/2` and `gcd/2` are actually needed
# Emit an ordered stream of the Farey sequence of order $order
# by recursively generating the mediants
def FS($order):
def f($l; $r; $n):
r($l.n + $r.n; $l.d + $r.d) as $m
| select($m.d <= $n)
| f($l; $m; $n), $m, f($m; $r; $n);
r(0;1) as $l
| r(1;1) as $r
| $l, f($l; $r; .), $r;
# Pretty-print Farey sequences of order $min up to and including order $max
def FareySequences($min; $max):
def rpp: "\(.n)/\(.d)";
def pp(s): [s|rpp] | join(" ");
range($min;$max+1)
| "F(\(.)): " + pp(FS(.));
# Use `count/1` for counting to save space
def count(s): reduce s as $_ (0; .+1);
def FareySequenceMembers($N):
count(FS($N));
# The tasks:
FareySequences(1;11),
"",
(range(100; 1001; 100) | "F\(.): \(FareySequenceMembers(.)|length) members" )
</syntaxhighlight>
''Invocation'': jq -r
<pre>
F(1): 0/1 1/1
F(2): 0/1 1/2 1/1
F(3): 0/1 1/3 1/2 2/3 1/1
F(4): 0/1 1/4 1/3 1/2 2/3 3/4 1/1
F(5): 0/1 1/5 1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 1/1
F(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
F(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
F(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
F(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
F(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
F(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
F100: 3045 members
F200: 12233 members
F300: 27399 members
F400: 48679 members
F500: 76117 members
F600: 109501 members
F700: 149019 members
F800: 194751 members
F900: 246327 members
F1000: 304193 members
</pre>
=={{header|Julia}}==
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