Problem 57720. The Yellowstone Permutation

Created by HH

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The Yellowstone Permutation is a sequence of positive integers, defined by the following rules:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>No term is repeated.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Given n terms, the next term, a(n+1), is always the smallest possible integer.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Every term, a(n), must be relatively prime to the previous term, a(n-1).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Every term, a(n), must have a common divisor greater than 1 with the term before the previous, a(n-2).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The first three terms of the sequence, after which we start applying the rules, are [1  2  3]. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Given a positive integer, n, return the n-th term of the sequence, a(n).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Example:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[n = 4;\na = 4]]></w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; "><div style="block-size: 264.659px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 132.33px; transform-origin: 406.996px 132.33px; vertical-align: baseline; "><div style="block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">The Yellowstone Permutation is a sequence of positive integers, defined by the following rules:</span></span></div><ul style="block-size: 81.7614px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.994px 40.8807px; transform-origin: 390.994px 40.8807px; margin-top: 10px; margin-bottom: 20px; "><li style="background-position: 0px 50%; block-size: 20.4403px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.997px 10.2131px; text-align: left; transform-origin: 362.997px 10.2202px; white-space: pre-wrap; margin-left: 56px; "><span style="background-position: 0% 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">No term is repeated.</span></span></li><li style="background-position: 0px 50%; block-size: 20.4403px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.997px 10.2131px; text-align: left; transform-origin: 362.997px 10.2202px; white-space: pre-wrap; margin-left: 56px; "><span style="background-position: 0% 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Given n terms, the next term, a(n+1), is always the smallest possible integer.</span></span></li><li style="background-position: 0px 50%; block-size: 20.4403px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.997px 10.2131px; text-align: left; transform-origin: 362.997px 10.2202px; white-space: pre-wrap; margin-left: 56px; "><span style="background-position: 0% 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Every term, a(n), must be relatively prime to the previous term, a(n-1).</span></span></li><li style="background-position: 0px 50%; block-size: 20.4403px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.997px 10.2131px; text-align: left; transform-origin: 362.997px 10.2202px; white-space: pre-wrap; margin-left: 56px; "><span style="background-position: 0% 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Every term, a(n), must have a common divisor greater than 1 with the term before the previous, a(n-2).</span></span></li></ul><div style="block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">The first three terms of the sequence, after which we start applying the rules, are [1  2  3]. </span></span></div><div style="block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Given a positive integer, n, return the n-th term of the sequence, a(n).</span></span></div><div style="block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Example:</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 40.8807px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.991px 20.4403px; transform-origin: 403.999px 20.4403px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4403px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.909091px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.909091px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.909091px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.909091px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.991px 10.2131px; transform-origin: 403.999px 10.2202px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">n = 4;</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4403px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.909091px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.909091px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.909091px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.909091px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.991px 10.2131px; transform-origin: 403.999px 10.2202px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">a = 4</span></span></div></div></div></div>

Solve

Solution Stats

8 Solutions
7 Solvers

Last Solution submitted on Mar 13, 2023

Last 200 Solutions

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers7

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 57720. The Yellowstone Permutation

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers7

Suggested Problems

More from this Author42

Problem Tags

Community Treasure Hunt

Problem 57720. The Yellowstone Permutation

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers7

Suggested Problems

More from this Author42

Problem Tags

Community Treasure Hunt

Players