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id	title	challengeType	forumTopicId	dashedName
5900f4141000cf542c50ff26	Problem 167: Investigating Ulam sequences	5	301801	problem-167-investigating-ulam-sequences

--description--

For two positive integers a and b, the Ulam sequence U(a,b) is defined by {U{(a,b)}\_1} = a, {U{(a,b)}\_2} = b and for k > 2, {U{(a,b)}\_k} is the smallest integer greater than {U{(a,b)}\_{(k-1)}} which can be written in exactly one way as the sum of two distinct previous members of U(a,b).

For example, the sequence U(1,2) begins with

1, 2, 3 = 1 + 2, 4 = 1 + 3, 6 = 2 + 4, 8 = 2 + 6, 11 = 3 + 8

5 does not belong to it because 5 = 1 + 4 = 2 + 3 has two representations as the sum of two previous members, likewise 7 = 1 + 6 = 3 + 4.

Find \sum {U(2, 2n + 1)_k} for 2 ≤ n ≤ 10, where k = {10}^{11}.

--hints--

ulamSequences() should return 3916160068885.

assert.strictEqual(ulamSequences(), 3916160068885);

--seed--

--seed-contents--

function ulamSequences() {

  return true;
}

ulamSequences();

--solutions--

// solution required

1.1 KiB Raw Blame History