Problem 1472. nth Rational Number

Created by G K
Appears in Magic Numbers

Difficulty:Rate

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Return the nth rational number.
This is the inverse to Problem 1471. Index of a Rational number
The first ten positive rational numbers under the enumeration using cantors diagonalization argument are 1/1, 2/1, 1/2, 3/1, 2/2, 1/3, 4/1, 3/2, 2/3, 1/4.
Find the index of a positive rational number enumerated in this manner, i.e. the 6th rational number is 1/3.
Problem 2) Prev: 1471 Next: 1477

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Last Solution submitted on Jan 18, 2025

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Massimo Zanetti on 7 Oct 2016

Is that possible to have a ranking of the solutions based on their performing time? I think that the could be a method that is fast even if more sized.

Massimo Zanetti on 10 Oct 2016

Solution

provides inexpensive method. There is only one 2nd order polynomial solution and one division.

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