1.5 KiB
id, title, challengeType, forumTopicId, dashedName
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f5101000cf542c510022 | Problem 419: Look and say sequence | 5 | 302088 | problem-419-look-and-say-sequence |
--description--
The look and say sequence goes 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ...
The sequence starts with 1 and all other members are obtained by describing the previous member in terms of consecutive digits.
It helps to do this out loud:
1 is 'one one' → 11
11 is 'two ones' → 21
21 is 'one two and one one' → 1211
1211 is 'one one, one two and two ones' → 111221
111221 is 'three ones, two twos and one one' → 312211
...
Define A(n), B(n) and C(n) as the number of ones, twos and threes in the $n$'th element of the sequence respectively. One can verify that A(40) = 31\\,254, B(40) = 20\\,259 and C(40) = 11\\,625.
Find A(n), B(n) and C(n) for n = {10}^{12}. Give your answer modulo 2^{30} as a string and separate your values for A, B and C by a comma. E.g. for n = 40 the answer would be 31254,20259,11625.
--hints--
lookAndSaySequence() should return a string.
assert(typeof lookAndSaySequence() === 'string');
lookAndSaySequence() should return the string 998567458,1046245404,43363922.
assert.strictEqual(lookAndSaySequence(), '998567458,1046245404,43363922');
--seed--
--seed-contents--
function lookAndSaySequence() {
return true;
}
lookAndSaySequence();
--solutions--
// solution required