ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
1.2 KiB
id, title, challengeType, forumTopicId, dashedName
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f4f81000cf542c51000b | Problem 396: Weak Goodstein sequence | 5 | 302061 | problem-396-weak-goodstein-sequence |
--description--
For any positive integer n, the nth weak Goodstein sequence {g1, g2, g3, ...} is defined as:
g1 = n
for k > 1, gk is obtained by writing gk-1 in base k, interpreting it as a base k + 1 number, and subtracting 1.
The sequence terminates when gk becomes 0.
For example, the 6th weak Goodstein sequence is {6, 11, 17, 25, ...}: g1 = 6. g2 = 11 since 6 = 1102, 1103 = 12, and 12 - 1 = 11. g3 = 17 since 11 = 1023, 1024 = 18, and 18 - 1 = 17. g4 = 25 since 17 = 1014, 1015 = 26, and 26 - 1 = 25.
and so on.
It can be shown that every weak Goodstein sequence terminates.
Let G(n) be the number of nonzero elements in the nth weak Goodstein sequence. It can be verified that G(2) = 3, G(4) = 21 and G(6) = 381. It can also be verified that ΣG(n) = 2517 for 1 ≤ n < 8.
Find the last 9 digits of ΣG(n) for 1 ≤ n < 16.
--hints--
euler396() should return 173214653.
assert.strictEqual(euler396(), 173214653);
--seed--
--seed-contents--
function euler396() {
return true;
}
euler396();
--solutions--
// solution required