freeCodeCamp

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id	challengeType	title	forumTopicId
5900f4ab1000cf542c50ffbe	5	Problem 319: Bounded Sequences	301975

Description

Let x1, x2,..., xn be a sequence of length n such that: x1 = 2 for all 1 < i ≤ n : xi-1 < xi for all i and j with 1 ≤ i, j ≤ n : (xi) j < (xj + 1)i

There are only five such sequences of length 2, namely: {2,4}, {2,5}, {2,6}, {2,7} and {2,8}. There are 293 such sequences of length 5; three examples are given below: {2,5,11,25,55}, {2,6,14,36,88}, {2,8,22,64,181}.

Let t(n) denote the number of such sequences of length n. You are given that t(10) = 86195 and t(20) = 5227991891.

Find t(1010) and give your answer modulo 109.

Instructions

Tests

tests:
  - text: <code>euler319()</code> should return 268457129.
    testString: assert.strictEqual(euler319(), 268457129);

Challenge Seed

function euler319() {
  // Good luck!
  return true;
}

euler319();

Solution

// solution required

1.2 KiB Raw Blame History