21 lines
520 B
Markdown
21 lines
520 B
Markdown
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Nice algorithm if you see the pattern in the numerators and denominators.
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~~~
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denom(n+1) = denom(n) + numer(n) * frac(n)
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numer(n+1) = denom(n)
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~~~
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and the fraction at position n is calculated by ([OEIS-A003417](https://oeis.org/A003417)):
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~~~
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int GetFrac(int idx)
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{
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if (idx == 0) return 2;
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if ((idx-1) % 3 == 0) return 1;
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if ((idx-1) % 3 == 1) return ((idx+1)/3)*2;
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if ((idx-1) % 3 == 2) return 1;
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return 2;
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}
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~~~
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The rest is just multiplication and long addition (we exceed the 64bit range) a hundred times ...
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