Problem 52574. Easy Sequences 8: Triangles with integer sides and prime perimeters

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>The triangle below is special.</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=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"105\"/><w:attr w:name=\"width\" w:val=\"175\"/><w:attr w:name=\"verticalAlign\" w:val=\"middle\"/><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>It has integer sides and a prime perimeter.  </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 an integer \"n\" we want to know </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>how many triangles can be formed such that the sides are integers and the perimeters are primes less than or equal to the nearest prime to \"n\"</w:t></w:r><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>The nearest prime number is defined as:</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>\"n\" if \"n\" itself is prime;</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>either the previous prime before or the next prime after \"n\", whichever has lesser distance to \"n\"; or</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>the previous prime before \"n\" if the previous and next primes are equidistant to \"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>As an example, lets consider \"n = 9\". The nearest prime is 7 because 9 is equidistant between 7 and 11. The primes less than equal to 7 are [2 3 5 7].  There are no integral triangles that can be formed with perimeter 2. For 3 there is one, namely [1 1 1]. For 5 there is one, [1 2 2]. And for 7 there are 2, [1 3 3] and [2 2 3] . So, the total number of prime perimetered integral triangles that can be formed when n = 9 is 4.</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>NOTE: Rotations and reflections are irrelevant and counted only 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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: 451.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 225.65px; transform-origin: 407px 225.65px; 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: 91px 8px; transform-origin: 91px 8px; unicode-bidi: normal; "><span style="">The triangle below is special.</span></span></div><div style="block-size: 105px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: middle;width: 175px;height: 105px" 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" data-image-state="image-loaded" width="175" height="105"></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: 136.5px 8px; transform-origin: 136.5px 8px; unicode-bidi: normal; "><span style="">It has integer sides and a prime perimeter.  </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: 118.5px 8px; transform-origin: 118.5px 8px; unicode-bidi: normal; "><span style="">Given an integer "n" we want to know </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: 264.5px 8px; transform-origin: 264.5px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">how many triangles can be formed such that the sides are integers and the perimeters are primes less than or equal to the nearest prime to "n"</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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; "><span style="">. </span></span></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: 128px 8px; transform-origin: 128px 8px; unicode-bidi: normal; "><span style="">The nearest prime number is defined as:</span></span></div><ul style="block-size: 61.3px; counter-reset: list-item 0; 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: 391px 30.65px; transform-origin: 391px 30.65px; margin-top: 10px; margin-bottom: 20px; "><li style="block-size: 20.4333px; counter-reset: none; 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: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 70.5px 8px; transform-origin: 70.5px 8px; unicode-bidi: normal; "><span style="">"n" if "n" itself is prime;</span></span></li><li style="block-size: 20.4333px; counter-reset: none; 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: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 311.5px 8px; transform-origin: 311.5px 8px; unicode-bidi: normal; "><span style="">either the previous prime before or the next prime after "n", whichever has lesser distance to "n"; or</span></span></li><li style="block-size: 20.4333px; counter-reset: none; 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: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 260.5px 8px; transform-origin: 260.5px 8px; unicode-bidi: normal; "><span style="">the previous prime before "n" if the previous and next primes are equidistant to "n".</span></span></li></ul><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: 380.5px 8px; transform-origin: 380.5px 8px; unicode-bidi: normal; "><span style="">As an example, lets consider "n = 9". The nearest prime is 7 because 9 is equidistant between 7 and 11. The primes less than equal to 7 are [2 3 5 7].  There are no integral triangles that can be formed with perimeter 2. For 3 there is one, namely [1 1 1]. For 5 there is one, [1 2 2]. And for 7 there are 2, [1 3 3] and [2 2 3] . So, the total number of prime perimetered integral triangles that can be formed when n = 9 is 4.</span></span></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: 221.5px 8px; transform-origin: 221.5px 8px; unicode-bidi: normal; "><span style="">NOTE: Rotations and reflections are irrelevant and counted only once.</span></span></div></div></div>

The triangle below is special.

It has integer sides and a prime perimeter.  
Given an integer "n" we want to know how many triangles can be formed such that the sides are integers and the perimeters are primes less than or equal to the nearest prime to "n". 
The nearest prime number is defined as:
"n" if "n" itself is prime;
either the previous prime before or the next prime after "n", whichever has lesser distance to "n"; or
the previous prime before "n" if the previous and next primes are equidistant to "n".
As an example, lets consider "n = 9". The nearest prime is 7 because 9 is equidistant between 7 and 11. The primes less than equal to 7 are [2 3 5 7].  There are no integral triangles that can be formed with perimeter 2. For 3 there is one, namely [1 1 1]. For 5 there is one, [1 2 2]. And for 7 there are 2, [1 3 3] and [2 2 3] . So, the total number of prime perimetered integral triangles that can be formed when n = 9 is 4.
NOTE: Rotations and reflections are irrelevant and counted only once.

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Problem 52574. Easy Sequences 8: Triangles with integer sides and prime perimeters

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Problem 52574. Easy Sequences 8: Triangles with integer sides and prime perimeters

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