n = 3
a = percentage = 5323
b = 10000
h = [1, 0, 1]
k = [0, 1, 0]
loop {
if a/b > 1
nxt = [a/b-1, a/b]
else
nxt = [a/b]
end
break if nxt.any?{|a_n|
h[n] = a_n*h[n-1] + h[n-2]
k[n] = a_n*k[n-1] + k[n-2]
(percentage - 10000.0*h[n]/k[n]).abs < 0.5
}
n,a,b = n+1, b, a%b
}
p k[n]
p h[n]/k[n].to_f
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