47 lines
817 B
Markdown
47 lines
817 B
Markdown
---
|
|
id: 5900f49d1000cf542c50ffaf
|
|
title: 'Problem 304: Primonacci'
|
|
challengeType: 5
|
|
forumTopicId: 301958
|
|
dashedName: problem-304-primonacci
|
|
---
|
|
|
|
# --description--
|
|
|
|
For any positive integer n the function next_prime(n) returns the smallest prime p such that p>n.
|
|
|
|
The sequence a(n) is defined by: a(1)=next_prime(1014) and a(n)=next_prime(a(n-1)) for n>1.
|
|
|
|
The fibonacci sequence f(n) is defined by: f(0)=0, f(1)=1 and f(n)=f(n-1)+f(n-2) for n>1.
|
|
|
|
The sequence b(n) is defined as f(a(n)).
|
|
|
|
Find ∑b(n) for 1≤n≤100 000. Give your answer mod 1234567891011.
|
|
|
|
# --hints--
|
|
|
|
`euler304()` should return 283988410192.
|
|
|
|
```js
|
|
assert.strictEqual(euler304(), 283988410192);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function euler304() {
|
|
|
|
return true;
|
|
}
|
|
|
|
euler304();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|