Problem 52283. Find numbers in the Popular Computing Z-sequence

Created by ChrisR

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{"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>Here’s a quick one. In 1977 the magazine </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Popular Computing</w:t></w:r><w:r><w:t> sought “problem situations for which the computer is the best (if not the only) tool for solution” and proposed the Z-sequence as a candidate “problem situation:”</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"a1 = a2 = 1\"/></w:customXmlPr><w:r><w:t>a_1 = a_2 = 1</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:attr w:name=\"altTextString\" w:val=\"a_n = |2 a_{n-2} + a_{n-1} – n|\"/></w:customXmlPr><w:r><w:t>a_n = |2 a_{n-2} + a_{n-1} – n|</w:t></w:r></w:customXml><w:r><w:t> for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"n &gt; 2\"/></w:customXmlPr><w:r><w:t>n &gt; 2</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Among the Z-sequence’s properties, the magazine staff pointed out that “successive values seem unpredictable; that is, the values jump around, but not too wildly” and “almost every integer appears as a term in the sequence sooner or later, except for a few numbers, such as 245, 449, 569, 575, and 903.”</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>Write a function to find the index of the first occurrence of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"k\"/></w:customXmlPr><w:r><w:t>k</w:t></w:r></w:customXml><w:r><w:t> (including the five numbers above) in the </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>Popular Computing </w:t></w:r><w:r><w:t>Z-sequence. </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: 20.4333px; 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: 195.817px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 97.9083px; transform-origin: 407px 97.9083px; vertical-align: baseline; "><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: 130.958px 7.79167px; transform-origin: 130.958px 7.79167px; unicode-bidi: normal; "><span style="">Here’s a quick one. In 1977 the magazine </span></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: 59.9167px 7.79167px; transform-origin: 59.9167px 7.79167px; unicode-bidi: normal; "><span style="font-style: italic; ">Popular Computing</span></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: 192.533px 7.79167px; transform-origin: 192.533px 7.79167px; unicode-bidi: normal; "><span style=""> sought “problem situations for which the computer is the best (if not the only) tool for solution” and proposed the Z-sequence as a candidate “problem situation:”</span></span></div><div style="block-size: 21.8167px; 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 10.9083px; text-align: left; transform-origin: 384px 10.9083px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-6px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJEAAAAoCAYAAAD+HRieAAACw0lEQVR4nO2ZUbXCMAyGPw9zMAMzMAUowMEc4OBamAYk4AEL0zAL3IeS0wzaDdbCKOQ7py/s3nbJ/qRJC4ZhGIZhGIZhGIZhfDY1sN/6JYwyqYEeuADHjd/FKIwK+MOJR4aJyHiKA9Bch4nISMZEZCRjIjKSeYmIGqDD7Zvt9bcWv49+K9LmHvDtrvhit9VLvYGsImqAEzDgHNfi2r+zWqjOsZCixn201NHeTvwEFc7OEdextDj7td2vOEPJYXeO98omov11ogHn1NAiQ+oiAVqmbeba0a1cv8GJZ+ReiCdeFzyQx+4c2SPLXHMC0ov8pSwSIVcmWrPNzgkIvIjOK+Z+hBx259hmk0W0U5OEHFkvPC+VGieeC+5jhBgWnn8LSSKq8I6MTSBZaiScpfTflVR0S5YZI8+Xgkc3H6XfOSWJ6KAmiAlAnH2KPG/xBWgpHYyuw2K1lPgmFDxShOua6UxZQaRJEpFkoTmByAKhlC6tr6T9NSLaojs7Mp9ddYa+9c2BqbMrfBDF/Bij+O5sSSAwjbS5KJO/WyOiLboz+Z/YR9cZ+nbeM/edmr5/mtvyY+9RbHemHRX6+B0+GpfqoRQRvbs706INdZvSscXqoZiNa0RUfHc2J6I9bouStC8R2xPOWikiejdzImpwdvdMg2fP8lb1yqOAV7NaRDoFn3DOqnAikfMiicj+OmKLlCQi8HYN+AwmgdPig2dQv89lGBHm2gPPLalI3BrFWbd7rDhs5LEFShNRx73durvSflkSEPirodJomNo6srJQ3+GyT8d9wfjopWtpIgJnU6yekjrtEXukhiqtvZeL5pw3AEmUKKIcVDjbv+kkfzN+VURHyqyDPpJfFFFPWEA7nmvzjSu/JqJYp9pGfjcW0EcBv5DaQ52dHqVfxr4d3eHoE9RvTedyjjY3DMMwDMMwDMMwDMMwPp1/BgCgoCGZtUIAAAAASUVORK5CYII=" alt="a1 = a2 = 1" style="width: 72.5px; height: 20px;" width="72.5" 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: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; "><span style=""> and </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="a_n = |2 a_{n-2} + a_{n-1} – n|" style="width: 134.5px; height: 20px;" width="134.5" 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: 12.05px 7.79167px; transform-origin: 12.05px 7.79167px; unicode-bidi: normal; "><span style=""> for </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="n > 2" style="width: 36.5px; height: 18px;" width="36.5" height="18"></span></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: 383.65px 7.79167px; transform-origin: 383.65px 7.79167px; unicode-bidi: normal; "><span style="">Among the Z-sequence’s properties, the magazine staff pointed out that “successive values seem unpredictable; that is, the values jump around, but not too wildly” and “almost every integer appears as a term in the sequence sooner or later, except for a few numbers, such as 245, 449, 569, 575, and 903.”</span></span></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: 178.775px 7.79167px; transform-origin: 178.775px 7.79167px; unicode-bidi: normal; "><span style="">Write a function to find the index of the first occurrence of </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">k</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: 129.925px 7.79167px; transform-origin: 129.925px 7.79167px; unicode-bidi: normal; "><span style=""> (including the five numbers above) in the </span></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: 61.8583px 7.79167px; transform-origin: 61.8583px 7.79167px; unicode-bidi: normal; "><span style="font-style: italic; ">Popular Computing </span></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: 40.8417px 7.79167px; transform-origin: 40.8417px 7.79167px; unicode-bidi: normal; "><span style="">Z-sequence. </span></span></div></div></div>

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Problem 52283. Find numbers in the Popular Computing Z-sequence

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