7d9496e52c
* fix: clean-up Project Euler 361-380 * fix: improve wording Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: remove unnecessary paragraph * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
58 lines
1.6 KiB
Markdown
58 lines
1.6 KiB
Markdown
---
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id: 5900f4d51000cf542c50ffe8
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title: 'Problem 361: Subsequence of Thue-Morse sequence'
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challengeType: 5
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forumTopicId: 302022
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dashedName: problem-361-subsequence-of-thue-morse-sequence
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---
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# --description--
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The Thue-Morse sequence $\\{T_n\\}$ is a binary sequence satisfying:
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- $T_0 = 0$
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- $T_{2n} = T_n$
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- $T_{2n + 1} = 1 - T_n$
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The first several terms of $\\{T_n\\}$ are given as follows: $01101001\color{red}{10010}1101001011001101001\ldots$.
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We define $\\{A_n\\}$ as the sorted sequence of integers such that the binary expression of each element appears as a subsequence in $\\{T_n\\}$. For example, the decimal number 18 is expressed as 10010 in binary. 10010 appears in $\\{T_n\\}$ ($T_8$ to $T_{12}$), so 18 is an element of $\\{A_n\\}$. The decimal number 14 is expressed as 1110 in binary. 1110 never appears in $\\{T_n\\}$, so 14 is not an element of $\\{A_n\\}$.
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The first several terms of $A_n$ are given as follows:
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$$\begin{array}{cr}
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n & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & \ldots \\\\
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A_n & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 9 & 10 & 11 & 12 & 13 & 18 & \ldots
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\end{array}$$
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We can also verify that $A_{100} = 3251$ and $A_{1000} = 80\\,852\\,364\\,498$.
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Find the last 9 digits of $\displaystyle\sum_{k = 1}^{18} A_{{10}^k}$.
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# --hints--
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`subsequenceOfThueMorseSequence()` should return `178476944`.
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```js
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assert.strictEqual(subsequenceOfThueMorseSequence(), 178476944);
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```
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# --seed--
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## --seed-contents--
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```js
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function subsequenceOfThueMorseSequence() {
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return true;
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}
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subsequenceOfThueMorseSequence();
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```
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# --solutions--
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```js
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// solution required
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```
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