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A229941
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Sequence of triples: the 10 solutions of 1/p + 1/q + 1/r = 1/2 with 0 < p <= q <= r, lexicographically sorted.
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2
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3, 7, 42, 3, 8, 24, 3, 9, 18, 3, 10, 15, 3, 12, 12, 4, 5, 20, 4, 6, 12, 4, 8, 8, 5, 5, 10, 6, 6, 6
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OFFSET
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1,1
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COMMENTS
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As noted by John Baez, "each of [the 10 solutions of 1/p + 1/q + 1/r = 1/2] gives a way for three regular polygons to snugly meet at a point".
Among the 14 4-term Egyptian fractions with unit sum, there are 10 of the form 1/2 + 1/p + 1/q + 1/r.
Also integer values of length, width and height of a rectangular prism whose surface area is equal to its volume: pqr = 2(pq+pr+qr). - John Rafael M. Antalan, Jul 05 2015
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LINKS
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EXAMPLE
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a(1) = 3, a(2) = 7, a(3) = 42, since 1/3 + 1/7 + 1/42 = 1/2.
The 10 solutions are:
3, 7, 42;
3, 8, 24;
3, 9, 18;
3, 10, 15;
3, 12, 12;
4, 5, 20;
4, 6, 12;
4, 8, 8;
5, 5, 10;
6, 6, 6
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MATHEMATICA
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{p, q, r} /. {ToRules[Reduce[0 < p <= q <= r && 1/p + 1/q + 1/r == 1/2, {p, q, r}, Integers] ]} // Flatten
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CROSSREFS
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KEYWORD
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easy,fini,nonn,full,tabf
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AUTHOR
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STATUS
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approved
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