* fix: clean-up Project Euler 281-300 * fix: missing image extension * fix: missing power Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: missing subscript Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
1.1 KiB
1.1 KiB
id, title, challengeType, forumTopicId, dashedName
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f4951000cf542c50ffa8 | Problem 297: Zeckendorf Representation | 5 | 301949 | 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 < {10}^6
, \sum z(n) = 7\\,894\\,453
.
Find \sum z(n)
for 0 < n < {10}^{17}
.
--hints--
zeckendorfRepresentation()
should return 2252639041804718000
.
assert.strictEqual(zeckendorfRepresentation(), 2252639041804718000);
--seed--
--seed-contents--
function zeckendorfRepresentation() {
return true;
}
zeckendorfRepresentation();
--solutions--
// solution required