Problem 53740. Easy Sequences 59: Almost Twin Primes

Created by Ramon Villamangca

Solve Later

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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: 234.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 117.25px; transform-origin: 407px 117.25px; vertical-align: baseline; "><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: 70.5px 8px; transform-origin: 70.5px 8px; unicode-bidi: normal; ">A positive integer pair <img src="data:image/png;base64,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" style="width: 67px; height: 18.5px;" width="67" 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: 280.075px 8px; transform-origin: 280.075px 8px; unicode-bidi: normal; ">, is called an "almost twin prime pair", if one of the pair is a prime and the other is either a prime or a semiprime. A <a target='_blank' href = "https://en.wikipedia.org/wiki/Semiprime">semiprime</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: 255.5px 8px; transform-origin: 255.5px 8px; unicode-bidi: normal; "> is a natural number that is a product of only two and exactly two (not necessarily distinct) prime numbers (e.g. 4<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; ">, 6<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; ">, 9<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,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" style="width: 18px; height: 18px;" width="18" 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,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" style="width: 18px; height: 18px;" width="18" 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,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" style="width: 18px; height: 18px;" width="18" 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,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" style="width: 18px; height: 18px;" width="18" 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,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" style="width: 18px; height: 18px;" width="18" 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,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" style="width: 18px; height: 18px;" width="18" 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: 10.5px 8px; transform-origin: 10.5px 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: 228px 8px; transform-origin: 228px 8px; unicode-bidi: normal; ">Listed below are all almost twin prime pairs with no element greater than <img src="data:image/png;base64,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" style="width: 25.5px; height: 18px;" width="25.5" 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: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; ">:</div><div style="block-size: 81.5px; 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 40.75px; text-align: left; transform-origin: 384px 40.75px; 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: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 440.5px; height: 81.5px;" width="440.5" height="81.5"></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: 94.5px 8px; transform-origin: 94.5px 8px; unicode-bidi: normal; ">Our task in this exercise is, to <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: 262.5px 8px; transform-origin: 262.5px 8px; unicode-bidi: normal; ">create a function that counts the number of almost twin prime pairs whose elements are less than or equal to a given limit <img src="data:image/png;base64,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" 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: 46px 8px; transform-origin: 46px 8px; unicode-bidi: normal; "> Therefore for <img src="data:image/png;base64,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" style="width: 51.5px; height: 18px;" width="51.5" 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: 87.5px 8px; transform-origin: 87.5px 8px; unicode-bidi: normal; ">, our function should return <img src="data:image/png;base64,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" style="width: 18px; height: 18px;" width="18" 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></div>

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Problem 53740. Easy Sequences 59: Almost Twin Primes

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Problem 53740. Easy Sequences 59: Almost Twin Primes

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