51 lines
758 B
Markdown
51 lines
758 B
Markdown
|
---
|
||
|
|
id: 5900f53c1000cf542c51004e
|
||
|
|
title: 'Problem 463: A weird recurrence relation'
|
||
|
|
challengeType: 5
|
||
|
|
forumTopicId: 302138
|
||
|
|
dashedName: problem-463-a-weird-recurrence-relation
|
||
|
|
---
|
||
|
|
|
||
|
|
# --description--
|
||
|
|
|
||
|
|
The function $f$ is defined for all positive integers as follows:
|
||
|
|
|
||
|
|
$f(1)=1$
|
||
|
|
|
||
|
|
$f(3)=3$
|
||
|
|
|
||
|
|
$f(2n)=f(n)$
|
||
|
|
|
||
|
|
$f(4n + 1)=2f(2n + 1) - f(n)$
|
||
|
|
|
||
|
|
$f(4n + 3)=3f(2n + 1) - 2f(n)$
|
||
|
|
|
||
|
|
The function $S(n)$ is defined as $\\sum\_{i=1}^{n}f(i)$. $S(8)=22$ and $S(100)=3604$. Find $S(3^{37})$. Give the last 9 digits of your answer.
|
||
|
|
|
||
|
|
# --hints--
|
||
|
|
|
||
|
|
`euler463()` should return 808981553.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.strictEqual(euler463(), 808981553);
|
||
|
|
```
|
||
|
|
|
||
|
|
# --seed--
|
||
|
|
|
||
|
|
## --seed-contents--
|
||
|
|
|
||
|
|
```js
|
||
|
|
function euler463() {
|
||
|
|
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
euler463();
|
||
|
|
```
|
||
|
|
|
||
|
|
# --solutions--
|
||
|
|
|
||
|
|
```js
|
||
|
|
// solution required
|
||
|
|
```
|