freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-343-fractional-sequences.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f4c41000cf542c50ffd6	Problem 343: Fractional Sequences	5	302002	problem-343-fractional-sequences

--description--

For any positive integer k, a finite sequence a_i of fractions \frac{x_i}{y_i} is defined by:

• a_1 = \displaystyle\frac{1}{k} and
• a_i = \displaystyle\frac{(x_{i - 1} + 1)}{(y_{i - 1} - 1)} reduced to lowest terms for i > 1.

When a_i reaches some integer n, the sequence stops. (That is, when y_i = 1.)

Define f(k) = n.

For example, for k = 20:

\frac{1}{20} → \frac{2}{19} → \frac{3}{18} = \frac{1}{6} → \frac{2}{5} → \frac{3}{4} → \frac{4}{3} → \frac{5}{2} → \frac{6}{1} = 6

So f(20) = 6.

Also f(1) = 1, f(2) = 2, f(3) = 1 and \sum f(k^3) = 118\\,937 for 1 ≤ k ≤ 100.

Find \sum f(k^3) for 1 ≤ k ≤ 2 × {10}^6.

--hints--

fractionalSequences() should return 269533451410884200.

assert.strictEqual(fractionalSequences(), 269533451410884200);

--seed--

--seed-contents--

function fractionalSequences() {

  return true;
}

fractionalSequences();

--solutions--

// solution required