Problem 58229. Easy Sequences 112: Almost Golden Integer Rectangles 1

Created by Ramon Villamangca

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>A </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Golden_rectangle\"><w:r><w:rPr><w:b/></w:rPr><w:t>golden rectangle</w:t></w:r></w:hyperlink><w:r><w:t> is a rectangle whose side lengths are in the golden ratio, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\phi/1</w:t></w:r></w:customXml><w:r><w:t>, where: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\phi=\\frac^{\\sqrt{5}+1}_2=1.61803398...</w:t></w:r></w:customXml><w:r><w:t>.</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>                                                                       </w:t></w:r><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"128\"/><w:attr w:name=\"width\" w:val=\"204\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The ancient Greeks consider the golden rectangle as the most aesthetically pleasing rectangular shape. Unfortunately for the ancients this ratio cannot be achieved if the sides are rational numbers let alone integers.</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:rPr><w:b/></w:rPr><w:t>In this problem we are asked to find the perimeter of the rectangle with integer sides with area within the given area interval </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[A_1,\\ A_2]</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, and in which the side ratio is as close as possible to the golden ratio, that is the absolute value, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>|\\frac^b_a-\\phi|</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, is minimized.</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>For example, if </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>A_1=20000</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>A_2=30000</w:t></w:r></w:customXml><w:r><w:t>, the correct dimensions should be </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[123,\\ 199]</w:t></w:r></w:customXml><w:r><w:t>, therefore the perimeter should be </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>p=644</w:t></w:r></w:customXml><w:r><w:t>:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[>>  A1 = 20000; A2 = 30000; phi = (sqrt(5)+1)/2; a = Inf;\n>>  for i = 1:A2\n      for j = ceil(A1/i):floor(A2/i)\n         r = max(j/i,i/j);\n         if abs(r-phi) < a\n            p = 2 * (i + j);\n            a = abs(r-phi);\n         end\n      end\n    end\n>> p\np =\n  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","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: 20.4333px; 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: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 633.133px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 316.567px; transform-origin: 407px 316.567px; vertical-align: baseline; "><div style="block-size: 31px; 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: 384px 15.5px; text-align: left; transform-origin: 384px 15.5px; 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: 6.5px 8px; transform-origin: 6.5px 8px; unicode-bidi: normal; "><span style="">A </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Golden_rectangle"><span style=""><span style="font-weight: 700; ">golden rectangle</span></span></a><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: 182px 8px; transform-origin: 182px 8px; unicode-bidi: normal; "><span style=""> is a rectangle whose side lengths are in the golden ratio, </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 28px; height: 18.5px;" width="28" height="18.5"></span><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: 27px 8px; transform-origin: 27px 8px; unicode-bidi: normal; "><span style="">, where: </span></span><span style="vertical-align:-10px"><img src="data:image/png;base64,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" style="width: 159px; height: 31px;" width="159" height="31"></span><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: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "><span style="">.</span></span></div><div style="block-size: 133.5px; 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: 384px 66.75px; text-align: left; transform-origin: 384px 66.75px; 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: 142px 8px; transform-origin: 142px 8px; unicode-bidi: normal; "><span style="">                                                                       </span></span><img class="imageNode" style="vertical-align: baseline;width: 204px;height: 128px" 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data-image-state="image-loaded" width="204" height="128"></div><div style="block-size: 42px; 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: 384px 21px; text-align: left; transform-origin: 384px 21px; 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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; "><span style="">The ancient Greeks consider the golden rectangle as the most aesthetically pleasing rectangular shape. Unfortunately for the ancients this ratio cannot be achieved if the sides are rational numbers let alone integers.</span></span></div><div style="block-size: 72px; 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: 384px 36px; text-align: left; transform-origin: 384px 36px; 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: 371px 8px; transform-origin: 371px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">In this problem we are asked to find the perimeter of the rectangle with integer sides with area within the given area interval </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGkAAAAoCAYAAAD9htTzAAAEeklEQVR4Xu1bSa8OQRT1foDZykLEsBALIsSGLcJGghgjb2daShAiFoZgYyOGndggsTXEEpEIEhJWhlhZmf0Azok6UindXfX61a3v65fu5Ob1972uqnvvuXXq3qr+Rib119B7YGToNewVnNSD1IEgaALpUI3+T/D94w7YNqwqzoNim2uUu43vP4T/awLpNx5+DvkSNLqGzzeH1QMd0GsJdDxXoedafLe6agLEQKps1AFHdFFFToqBgcTpPRnyqoue83TmDPhVRUeZ7BooSO9gBGVdJmMG0Q0D7T3kMOS8kQIDA2kPDLri1jaCFK5vRvZm75Zr8FbIZcj+7L3/7XAgIM3EwG8h051RszoK0iro/cjZwERqxUQC6RKM2ecZtAH3d40MtOyWVD3fG8Aq2IrPJEUfeVwG7sX9VUtvGvTNWvGI61eMsBSfLZKg4iDdhyEsyj5CVBOcwf0xA0dadSm65ho0CmEdw8uKEYqCtA2G3ICQFlZC7jjjLPncAijSNdcfymnIUTeIVbAVA0nRdxYGMVVlbfHSGUfqI2hdyPBE1youlaXSlFsQBmLuqxhI4vAZngUcXJfVopvbYaTr7x4YJTK8IiCp4As5+xmMXe68aMXnOUHy6Vqzngzx2TjYioDE6KMxYR2hQpA2DnuGJ7pm0RomOV/xnWWGZw6S6IAgvAnCegc+q16yWnRzzSTR9S50+DPo9IIxI5iDxIKPl/769jE6RXcpGZ4ctRDtSiYZouuq4xnaswCimq8p2Kj/Fs9mzsrjCbaYgkSlWAvVJQWpGR7Xgo0Q7pHxKp1k1NG1Ai4lw2PazqTpOmQK5KAD6xv+xoLODKQmDvdnU0qGRzBZyevZkiCJrpsSm1iGp8O8nd6soX+euhkYW4/NQNL+XMyh/v5XLMMbBEjUj9HetHkqOlTwhTaTUV5Dwv1JFcKx9dgEJNFYbHAaRSrRtkpKRDXRHWlxTo1D/Nmbei8aiwUP+/MZIXUPT8tBit3ZT2bleC6m/708EXjIT8NjZzJNM0k1jLqPGR4DSnTN9JqJQezy0/DteDjlXQ+xTQzU7DPJP4ZIAckvaLk9tKYB2CaQ/MWbDmVfKc6tcj4BYqAx82RGFzuUDAtabg8dgMQyUFLpA0jssDArSASI/KyLs+hhTVRxqs8Nnme7pjZNINFRJ11/AqcNSNSfND3Ns+MF7u9BwtfV9ArWsuB5Nq1ro245809BmoJSz2YFybPL5DY1cVAAxCLURMmETpXZjVYAX9V8woEkB2yCtRYHcAkYRB8hxZ+ApJ5GTyiQtJaMxQFRj2Z+gEsCg2csJ9GtQarai/vk1pTMdv3rLkZ3pLlhftWZALHmCjdoWQwvhvBV4kUVzuPLLq1S8CogLN898zOoWIFsFSTj6ZeFKzeTWWb88DqaintudzGBmA3R20fhWGMGaTzKtmm7Ho12O2PYninuRUhXfhwQ1nChD1qf6PY/fWkTToXb9CAVdnib4XqQ2nitcJsepMIObzNcD1IbrxVu04NU2OFthutBauO1wm3+AB3KXDjOjVl5AAAAAElFTkSuQmCC" style="width: 52.5px; height: 20px;" width="52.5" height="20"></span><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: 285.5px 8px; transform-origin: 285.5px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">, and in which the side ratio is as close as possible to the golden ratio, that is the absolute value, </span></span><span style="vertical-align:-10px"><img src="data:image/png;base64,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" style="width: 47.5px; height: 29px;" width="47.5" height="29"></span><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: 49px 8px; transform-origin: 49px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">, is minimized.</span></span></div><div style="block-size: 43px; 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: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; 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: 48.5px 8px; transform-origin: 48.5px 8px; unicode-bidi: normal; "><span style="">For example, if </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" style="width: 73.5px; height: 20px;" width="73.5" height="20"></span><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: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; "><span style=""> and </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" style="width: 73.5px; height: 20px;" width="73.5" height="20"></span><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: 110.5px 8px; transform-origin: 110.5px 8px; unicode-bidi: normal; "><span style="">, the correct dimensions should be </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 69.5px; height: 18.5px;" width="69.5" height="18.5"></span><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: 101.092px 8px; transform-origin: 101.092px 8px; unicode-bidi: normal; "><span style="">, therefore the perimeter should be </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 53px; height: 18px;" width="53" height="18"></span><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: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "><span style="">:</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 265.633px; 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: 404px 132.817px; transform-origin: 404px 132.817px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; 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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; 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: 404px 10.2167px; transform-origin: 404px 10.2167px; 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: 228px 8.5px; tab-size: 4; transform-origin: 228px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">&gt;&gt;  A1 = 20000; A2 = 30000; phi = (sqrt(5)+1)/2; a = Inf;</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; 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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; 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: 404px 10.2167px; transform-origin: 404px 10.2167px; 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: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; ">&gt;&gt;  </span><span style="border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 16px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 16px 8.5px; ">for </span><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; ">i = 1:A2</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; 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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; 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: 404px 10.2167px; transform-origin: 404px 10.2167px; 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: 144px 8.5px; tab-size: 4; transform-origin: 144px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; ">      </span><span style="border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 16px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 16px 8.5px; ">for </span><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 104px 8.5px; transform-origin: 104px 8.5px; ">j = ceil(A1/i):floor(A2/i)</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; 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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; 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: 404px 10.2167px; transform-origin: 404px 10.2167px; 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: 104px 8.5px; tab-size: 4; transform-origin: 104px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">         r = max(j/i,i/j);</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; 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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; 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: 404px 10.2167px; transform-origin: 404px 10.2167px; 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: 104px 8.5px; tab-size: 4; transform-origin: 104px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; ">         </span><span style="border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; ">if </span><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; ">abs(r-phi) &lt; a</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; 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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; 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: 404px 10.2167px; transform-origin: 404px 10.2167px; 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: 112px 8.5px; tab-size: 4; transform-origin: 112px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">            p = 2 * (i + j);</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; 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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; 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: 404px 10.2167px; transform-origin: 404px 10.2167px; 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: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">            a = abs(r-phi);</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; 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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; 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: 404px 10.2167px; transform-origin: 404px 10.2167px; 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: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; ">         </span><span style="border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; ">end</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; 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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; 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: 404px 10.2167px; transform-origin: 404px 10.2167px; 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: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; ">      </span><span style="border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; ">end</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; 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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; 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: 404px 10.2167px; transform-origin: 404px 10.2167px; 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: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; ">    </span><span style="border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; ">end</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; 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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; 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: 404px 10.2167px; transform-origin: 404px 10.2167px; 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: 16px 8.5px; tab-size: 4; transform-origin: 16px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">&gt;&gt; p</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; 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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; 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: 404px 10.2167px; transform-origin: 404px 10.2167px; 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: 12px 8.5px; tab-size: 4; transform-origin: 12px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">p =</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; 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: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; 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: 404px 10.2167px; transform-origin: 404px 10.2167px; 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: 20px 8.5px; tab-size: 4; transform-origin: 20px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">  644</span></span></div></div></div></div>

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Problem 58229. Easy Sequences 112: Almost Golden Integer Rectangles 1

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Problem 58229. Easy Sequences 112: Almost Golden Integer Rectangles 1

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