freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-396-weak-goodstein-sequence.md

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 n$th weak Goodstein sequence \{g1, g2, g3, \ldots\}$ is defined as:

• g_1 = n
• for k > 1, g_k is obtained by writing g_{k - 1} in base k, interpreting it as a base k + 1 number, and subtracting 1.

The sequence terminates when g_k becomes 0.

For example, the 6$th weak Goodstein sequence is \{6, 11, 17, 25, \ldots\}$:

• g_1 = 6.
• g_2 = 11 since 6 = 110_2, 110_3 = 12, and 12 - 1 = 11.
• g_3 = 17 since 11 = 102_3, 102_4 = 18, and 18 - 1 = 17.
• g_4 = 25 since 17 = 101_4, 101_5 = 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 $n$th weak Goodstein sequence.

It can be verified that G(2) = 3, G(4) = 21 and G(6) = 381.

It can also be verified that \sum G(n) = 2517 for 1 ≤ n < 8.

Find the last 9 digits of \sum G(n) for 1 ≤ n < 16.

--hints--

weakGoodsteinSequence() should return 173214653.

assert.strictEqual(weakGoodsteinSequence(), 173214653);

--seed--

--seed-contents--

function weakGoodsteinSequence() {

  return true;
}

weakGoodsteinSequence();

--solutions--

// solution required