2018-09-30 22:01:58 +00:00
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---
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id: 5900f4311000cf542c50ff44
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title: 'Problem 197: Investigating the behaviour of a recursively defined sequence'
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2020-11-27 18:02:05 +00:00
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challengeType: 5
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2019-08-05 16:17:33 +00:00
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forumTopicId: 301835
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2018-09-30 22:01:58 +00:00
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---
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2020-11-27 18:02:05 +00:00
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# --description--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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Given is the function f(x) = ⌊230.403243784-x2⌋ × 10-9 ( ⌊ ⌋ is the floor-function),
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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the sequence un is defined by u0 = -1 and un+1 = f(un).
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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Find un + un+1 for n = 1012. Give your answer with 9 digits after the decimal point.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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# --hints--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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`euler197()` should return 1.710637717.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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```js
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assert.strictEqual(euler197(), 1.710637717);
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2018-09-30 22:01:58 +00:00
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```
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2020-11-27 18:02:05 +00:00
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# --seed--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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## --seed-contents--
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2018-09-30 22:01:58 +00:00
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```js
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function euler197() {
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2020-09-15 16:57:40 +00:00
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2018-09-30 22:01:58 +00:00
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return true;
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}
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euler197();
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```
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2020-11-27 18:02:05 +00:00
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# --solutions--
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2018-09-30 22:01:58 +00:00
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```js
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// solution required
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```
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