93 lines
5.4 KiB
HTML
93 lines
5.4 KiB
HTML
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<h2>An engineers' dream come true</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 263</h3><span style="width:300px;color:#666;">Published on Saturday, 7th November 2009, 01:00 am; Solved by 627</span></div>
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Consider the number 6. The divisors of 6 are: 1,2,3 and 6.<BR />
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Every number from 1 up to and including 6 can be written as a sum of distinct divisors of 6:<BR />
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1=1, 2=2, 3=1+2, 4=1+3, 5=2+3, 6=6.<BR />
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A number <var>n</var> is called a practical number if every number from 1 up to and including <var>n</var> can be expressed as a sum of distinct divisors of <var>n</var>.
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<P>
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A pair of consecutive prime numbers with a difference of six is called a sexy pair (since "sex" is the Latin word for "six"). The first sexy pair is (23, 29).
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<P>
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We may occasionally find a triple-pair, which means three consecutive sexy prime pairs, such that the second member of each pair is the first member of the next pair.
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We shall call a number <var>n</var> such that :
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<UL>
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<LI>(<var>n</var>-9, <var>n</var>-3), (<var>n</var>-3,<var>n</var>+3), (<var>n</var>+3, <var>n</var>+9) form a triple-pair, and
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<LI>the numbers <var>n</var>-8, <var>n</var>-4, <var>n</var>, <var>n</var>+4 and <var>n</var>+8 are all practical,
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</UL>
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an engineers’ paradise.
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</P>
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<P>
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Find the sum of the first four engineers’ paradises.
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