freeCodeCamp/problem-297-zeckendorf-representation.english.md at 1f310d8c5877a13cf67fbfaad323b4a558a0ac3c

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Valeriy 79d9012432 fix(curriculum): quotes in tests (#18828 )

* fix(curriculum): tests quotes

* fix(curriculum): fill seed-teardown

* fix(curriculum): fix tests and remove unneeded seed-teardown

2018-10-20 23:32:47 +05:30

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id, challengeType, title

id	challengeType	title
5900f4951000cf542c50ffa8	5	Problem 297: Zeckendorf Representation

Description

Each new term in the Fibonacci sequence is generated by adding the previous two terms. Starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.

Every positive integer can be uniquely written as a sum of nonconsecutive terms of the Fibonacci sequence. For example, 100 = 3 + 8 + 89. Such a sum is called the Zeckendorf representation of the number.

For any integer n>0, let z(n) be the number of terms in the Zeckendorf representation of n. Thus, z(5) = 1, z(14) = 2, z(100) = 3 etc. Also, for 0<n<106, ∑ z(n) = 7894453.

Find ∑ z(n) for 0<n<1017.

Instructions

Tests

tests:
  - text: <code>euler297()</code> should return 2252639041804718000.
    testString: assert.strictEqual(euler297(), 2252639041804718000, '<code>euler297()</code> should return 2252639041804718000.');

Challenge Seed

function euler297() {
  // Good luck!
  return true;
}

euler297();

Solution

// solution required

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