1.1 KiB
1.1 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3fa1000cf542c50ff0c | Problem 140: Modified Fibonacci golden nuggets | 5 | 301769 | problem-140-modified-fibonacci-golden-nuggets |
--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.
--hints--
euler140()
should return 5673835352990.
assert.strictEqual(euler140(), 5673835352990);
--seed--
--seed-contents--
function euler140() {
return true;
}
euler140();
--solutions--
// solution required