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id	challengeType	title	forumTopicId
5900f4d51000cf542c50ffe8	5	Problem 361: Subsequence of Thue-Morse sequence	302022

Description

The Thue-Morse sequence {Tn} is a binary sequence satisfying: T0 = 0 T2n = Tn T2n+1 = 1 - Tn

The first several terms of {Tn} are given as follows: 01101001100101101001011001101001....

We define {An} as the sorted sequence of integers such that the binary expression of each element appears as a subsequence in {Tn}. For example, the decimal number 18 is expressed as 10010 in binary. 10010 appears in {Tn} (T8 to T12), so 18 is an element of {An}. The decimal number 14 is expressed as 1110 in binary. 1110 never appears in {Tn}, so 14 is not an element of {An}.

The first several terms of An are given as follows: n0123456789101112…An012345691011121318…

We can also verify that A100 = 3251 and A1000 = 80852364498.

Find the last 9 digits of .

Instructions

Tests

tests:
  - text: <code>euler361()</code> should return 178476944.
    testString: assert.strictEqual(euler361(), 178476944);

Challenge Seed

function euler361() {
  // Good luck!
  return true;
}

euler361();

Solution

// solution required

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