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A120063
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Shortest side c of all integer-sided triangles with sides a<=b<=c and inradius n.
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4
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5, 10, 12, 15, 25, 24, 35, 30, 36, 39, 55, 45, 65, 63, 53, 60, 85, 68, 95, 75, 77, 88, 115, 85, 125, 130, 108, 105, 145, 106, 155, 120, 132, 170, 137, 135, 185, 190, 156, 150, 205, 154, 215, 165, 159, 230, 235, 170, 245, 195, 204, 195, 265, 204, 200, 195, 228, 290
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Terms a(11),..., a(100) computed by Thomas Mautsch (mautsch(AT)ethz.ch).
Empirically, 2*sqrt(3) < a(n)/n <= 5. The lower bound is provably tight, the upper bound seems to be achieved infinitely often, e.g, for prime n >= 5. It appears that a(p) = 5p for prime p != 3. - David W. Wilson, Jun 17 2006
Minimum of longest side occurring among all A120062(n) triangles having integer sides with integer inradius n.
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LINKS
| David W. Wilson, Table of n, a(n) for n = 1..10000
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EXAMPLE
| a(1)=5 because the only triangle with integer sides and inradius 1 is {3,4,5}; its longest side is 5.
a(2)=10: The triangles with inradius 2 are {5,12,13}, {6,8,10}, {6,25,29}, {7,15,20}, {9,10,17}. The minimum of their longest sides is min(13,10,29,20,17)=10.
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CROSSREFS
| See A120062 for sequences related to integer-sided triangles with integer inradius n.
Cf. A120062 [triangles with integer inradius], A120252 [primitive triangles with integer inradius], A057721 [maximum of longest sides], A058331 [maximum of shortest sides], A120064 [minimum of middle sides], A082044 [maximum of middle sides], A005408 [minimum of shortest sides], A007237.
Sequence in context: A162821 A059324 A112776 * A101839 A087920 A103676
Adjacent sequences: A120060 A120061 A120062 * A120064 A120065 A120066
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KEYWORD
| nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 13 2006
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