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id	challengeType	title	forumTopicId
5900f3fa1000cf542c50ff0c	5	Problem 140: Modified Fibonacci golden nuggets	301769

Description

Consider the infinite polynomial series AG(x) = xG1 + x2G2 + x3G3 + ..., where Gk is the kth term of the second order recurrence relation Gk = Gk−1 + Gk−2, G1 = 1 and G2 = 4; that is, 1, 4, 5, 9, 14, 23, ... . For this problem we shall be concerned with values of x for which AG(x) is a positive integer. The corresponding values of x for the first five natural numbers are shown below.

xAG(x) (√5−1)/41 2/52 (√22−2)/63 (√137−5)/144 1/25

We shall call AG(x) a golden nugget if x is rational, because they become increasingly rarer; for example, the 20th golden nugget is 211345365. Find the sum of the first thirty golden nuggets.

Instructions

Tests

tests:
  - text: <code>euler140()</code> should return 5673835352990.
    testString: assert.strictEqual(euler140(), 5673835352990);

Challenge Seed

function euler140() {
  // Good luck!
  return true;
}

euler140();

Solution

// solution required

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