Problem 53079. Easy Sequences 50: Blocked Gaussian Integers

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/Gaussian_integer\"><w:r><w:t>Gaussian Integer</w:t></w:r></w:hyperlink><w:r><w:t> is a complex number whose real and imaginary parts are both 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:t>A gaussian integer </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>z'</w:t></w:r></w:customXml><w:r><w:t> is said to be </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>blocked</w:t></w:r><w:r><w:t> with respect to another gaussian integer </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>z</w:t></w:r></w:customXml><w:r><w:t>, if the line segment connecting </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>z</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>z'</w:t></w:r></w:customXml><w:r><w:t> on the complex plane, pass through at least one more gaussian integer. In the figure below, 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>z=3+2i</w:t></w:r></w:customXml><w:r><w:t>, the red colored points represents the blocked gaussian integers with respect to </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>z</w:t></w:r></w:customXml><w:r><w:t>, While the green points represents unblocked gaussian 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:t> </w:t></w:r><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"-1\"/><w:attr w:name=\"width\" w:val=\"-1\"/><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>In the above figure, blocked gaussian points, </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>2i</w:t></w:r></w:customXml><w:r><w:t>, </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>1-2i</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>7+6i</w:t></w:r></w:customXml><w:r><w:t>, are shown. These points lie within the a square with side lengths </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=9</w:t></w:r></w:customXml><w:r><w:t>, in which </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>z=3+2i</w:t></w:r></w:customXml><w:r><w:t> is at the center. But these are not the only blocked gaussian points for this case. </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>-1-2i</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>7+2i</w:t></w:r></w:customXml><w:r><w:t> are also blocked points. The sum total of all blocked gaussian integers relative to </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>z=3+2i</w:t></w:r></w:customXml><w:r><w:t> and bounded by the square with side </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=9</w:t></w:r></w:customXml><w:r><w:t> and is </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>96+64i</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:rPr><w:b/></w:rPr><w:t>Given a gaussian integer </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>z</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, centered at a square of side </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</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, find the </w:t></w:r><w:r><w:rPr><w:b/><w:u/></w:rPr><w:t>absolute value of the sum</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> of all blocked gaussian integers around </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>z</w:t></w:r></w:customXml><w:r><w:t>,</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> with respect to </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>z</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, that lies within the square</w:t></w:r><w:r><w:t> (</w:t></w:r><w:r><w:rPr><w:u/></w:rPr><w:t>including</w:t></w:r><w:r><w:t>, any blocked gaussian points along the edges of the square). Therefore, in the example above, your program should output: </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>|\\ 96+64i\\ |=115.3776</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>Please round-off your answer to 4 decimal 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<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: 722.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 361.25px; transform-origin: 407px 361.25px; vertical-align: baseline; "><div style="block-size: 21px; 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 10.5px; text-align: left; transform-origin: 384px 10.5px; 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; ">A <a target='_blank' href = "https://en.wikipedia.org/wiki/Gaussian_integer">Gaussian Integer</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: 225px 8px; transform-origin: 225px 8px; unicode-bidi: normal; "> is a complex number whose real and imaginary parts are both integers.</div><div style="block-size: 84px; 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 42px; text-align: left; transform-origin: 384px 42px; 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: 61px 8px; transform-origin: 61px 8px; unicode-bidi: normal; ">A gaussian integer <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAkCAYAAABixKGjAAAA00lEQVRIie2VQQ3DMAxFH4cwGIESKIIhCIMyKINRKIZBKIdQGIZSaA+2parKdkgcaarypKi3b+f7u4FO51YEYNavOxHYgbGF+BtYadB5QLp+egujok26Blho5HURA+Ljr7OUik8q8EH8PJ8NSBWNs2qBK1ELVg0vJzwgXQ81wjmCCjfJciJ/m2oWZL3dmahMxjdGHJKRw5Lx8BYOiBXRWxhkeLbiK44/pRdix3YqcF2cRKFlZxFb9V0FbbBWuPpG9vBuiF2WINfcB+QmM//0MHRuxAHmODh6hQd5nwAAAABJRU5ErkJggg==" style="width: 11.5px; height: 18px;" width="11.5" height="18"><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: 42px 8px; transform-origin: 42px 8px; unicode-bidi: normal; "> is said to be <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: 28px 8px; transform-origin: 28px 8px; unicode-bidi: normal; ">blocked<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: 130.5px 8px; transform-origin: 130.5px 8px; unicode-bidi: normal; "> with respect to another gaussian integer z<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: 100px 8px; transform-origin: 100px 8px; unicode-bidi: normal; ">, if the line segment connecting z<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; "> and <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAkCAYAAABixKGjAAAA00lEQVRIie2VQQ3DMAxFH4cwGIESKIIhCIMyKINRKIZBKIdQGIZSaA+2parKdkgcaarypKi3b+f7u4FO51YEYNavOxHYgbGF+BtYadB5QLp+egujok26Blho5HURA+Ljr7OUik8q8EH8PJ8NSBWNs2qBK1ELVg0vJzwgXQ81wjmCCjfJciJ/m2oWZL3dmahMxjdGHJKRw5Lx8BYOiBXRWxhkeLbiK44/pRdix3YqcF2cRKFlZxFb9V0FbbBWuPpG9vBuiF2WINfcB+QmM//0MHRuxAHmODh6hQd5nwAAAABJRU5ErkJggg==" style="width: 11.5px; height: 18px;" width="11.5" height="18"><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: 311.5px 8px; transform-origin: 311.5px 8px; unicode-bidi: normal; "> on the complex plane, pass through at least one more gaussian integer. In the figure below, where <img src="data:image/png;base64,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" style="width: 63.5px; height: 18px;" width="63.5" height="18"><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; ">, the red colored points represents the blocked gaussian integers with respect to z<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: 113px 8px; transform-origin: 113px 8px; unicode-bidi: normal; ">, While the green points represents unblocked gaussian integers.</div><div style="block-size: 404.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; 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data-image-state="image-loaded"></div><div style="block-size: 84px; 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 42px; text-align: left; transform-origin: 384px 42px; 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: 143px 8px; transform-origin: 143px 8px; unicode-bidi: normal; ">In the above figure, blocked gaussian points, <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAkCAYAAAB15jFqAAABMUlEQVRYhe2WUZHDMAxEHwczKIEQCIIgCIMwKIOjEAyGEA6hYAylcPdha0buJbac5uvOO6Of1NYqWWlV6Oj46xhTDBfvOuthB6zA91u8gMWYY0t3dgvxIyV/J9TxZSDV50dLhQGY1bOB328+VfLMqfhqgVM6eKbfU5H6WjIrPGXNHLm+t2AlalqCNMhtpBYI6Xbwm4zXk/jVAg0jU0JIpEcyTOQNt99B+EjJAucyjLSNVhXSvaVmW2iYzxocsXmOtNTwivRjeGyWJm5WK66KhahjzfS1nlaPPsRsJITcsa5spWZCuME4JgPhQD468pbrFcKBWG2p5R2xsYRU6ykbaqNuqxnhTtToLAJ5h2o95U+AyRyEsLTAz3aqNoWdhtXnU/WW8OQz69T9j8alo6PjH+IHu6B/3OiYY/8AAAAASUVORK5CYII=" style="width: 14.5px; height: 18px;" width="14.5" height="18"><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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; ">, <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE4AAAAkCAYAAAAnxQwhAAABrklEQVRoge2Y4dGCMAyGnx3YoAuwABM4gRt8G7gBKzADI7CDKzgDK/j9KDlqVQqh6pXLc5fzDqVN3tY0KRiGYRiG8RscUP3aCQUV0EzmlO+qcEAH3IFaO8gPqIEB73doN9aJUQHj9E63ZeKKWTCxUoQ78SxYbKfEGE30+9UTX6bPK2UJJztl4HFnnXjeganU005jnTWOXChLuBa/2O9ECcX7+6QjpQk3suxn+DfuP+lIScLJQZbChFMi8Vyi51J+SI4fJlNxNOEc7+Op8AdBmAdb7URHE+6Mj2VpJ4Uxp8qWVYMcQTjZTUux9Gys316RQ7iw7dFajkWTojbObTHSMajzG+QRLq7CNbb3BKzw7Vbq1K2DOVMCL5JDOOkb99iuIPDCD6S7hWyp6Qg5rmOdaDDnwHHvpKULt0U0yFgclyxcS1q0Jvg+zMWqxj6kVOHO+MNg6fKyxl8ICGGscnF7ffHeKkoUTorcHu//K5Mro/DQkfwmtytXlAWww69aluP5S4hoa2zkcUf2wfMbimsnx5wfYus0A34Jx7YSJ+5DpWzq2dFqGYZhGIZhGMah+AfDPNsDmA7cKwAAAABJRU5ErkJggg==" style="width: 39px; height: 18px;" width="39" height="18"><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; "> and <img src="data:image/png;base64,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" style="width: 39px; height: 18px;" width="39" height="18"><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: 168px 8px; transform-origin: 168px 8px; unicode-bidi: normal; ">, are shown. These points lie within the a square with side lengths <img src="data:image/png;base64,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" style="width: 36.5px; height: 18px;" width="36.5" height="18"><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: 31px 8px; transform-origin: 31px 8px; unicode-bidi: normal; ">, in which <img src="data:image/png;base64,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" style="width: 63.5px; height: 18px;" width="63.5" height="18"><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: 256.5px 8px; transform-origin: 256.5px 8px; unicode-bidi: normal; "> is at the center. But these are not the only blocked gaussian points for this case. <img src="data:image/png;base64,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" style="width: 49.5px; height: 18px;" width="49.5" height="18"><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; "> and <img src="data:image/png;base64,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" style="width: 39px; height: 18px;" width="39" height="18"><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: 258.5px 8px; transform-origin: 258.5px 8px; unicode-bidi: normal; "> are also blocked points. The sum total of all blocked gaussian integers relative to <img src="data:image/png;base64,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" style="width: 63.5px; height: 18px;" width="63.5" height="18"><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; "> and bounded by the square with side <img src="data:image/png;base64,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" style="width: 36.5px; height: 18px;" width="36.5" height="18"><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: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; "> and is <img src="data:image/png;base64,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" style="width: 54px; height: 18px;" width="54" height="18"><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; ">.</div><div style="block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 90px 8px; transform-origin: 90px 8px; unicode-bidi: normal; ">Given a gaussian integer z<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: 105px 8px; transform-origin: 105px 8px; unicode-bidi: normal; ">, centered at a square of side 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: 33px 8px; transform-origin: 33px 8px; unicode-bidi: normal; ">, find the <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: 91px 8px; transform-origin: 91px 8px; unicode-bidi: normal; ">absolute value of the sum<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: 51px 8px; transform-origin: 51px 8px; unicode-bidi: normal; "> of all blocked gaussian integers around z<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="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: 56.5px 8px; transform-origin: 56.5px 8px; unicode-bidi: normal; "> with respect to z<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: 95px 8px; transform-origin: 95px 8px; unicode-bidi: normal; ">, that lies within the square<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: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; "> (<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: 28px 8px; transform-origin: 28px 8px; unicode-bidi: normal; ">including<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: 95.5px 8px; transform-origin: 95.5px 8px; unicode-bidi: normal; ">, any blocked gaussian points along the edges of the square). Therefore, in the example above, your program should output: <img src="data:image/png;base64,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" style="width: 153px; height: 18.5px;" width="153" height="18.5"><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; ">.</div><div style="block-size: 21px; 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 10.5px; text-align: left; transform-origin: 384px 10.5px; 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: 157.5px 8px; transform-origin: 157.5px 8px; unicode-bidi: normal; ">Please round-off your answer to 4 decimal places.</div></div></div>

A Gaussian Integer is a complex number whose real and imaginary parts are both integers.
A gaussian integer  is said to be blocked with respect to another gaussian integer , if the line segment connecting  and  on the complex plane, pass through at least one more gaussian integer. In the figure below, where , the red colored points represents the blocked gaussian integers with respect to , While the green points represents unblocked gaussian integers.
                                                  
In the above figure, blocked gaussian points, ,  and , are shown. These points lie within the a square with side lengths , in which  is at the center. But these are not the only blocked gaussian points for this case.  and  are also blocked points. The sum total of all blocked gaussian integers relative to  and bounded by the square with side  and is .
Given a gaussian integer , centered at a square of side , find the absolute value of the sum of all blocked gaussian integers around , with respect to , that lies within the square (including, any blocked gaussian points along the edges of the square). Therefore, in the example above, your program should output: .
Please round-off your answer to 4 decimal places.

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Problem 53079. Easy Sequences 50: Blocked Gaussian Integers

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Problem 53079. Easy Sequences 50: Blocked Gaussian Integers

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