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id	challengeType	title	forumTopicId
5900f4951000cf542c50ffa8	5	Problem 297: Zeckendorf Representation	301949

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);

Challenge Seed

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

euler297();

Solution

// solution required

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