A120064 Shortest side b of all integer-sided triangles with sides a<=b<=c and inradius n.
4, 8, 10, 14, 20, 20, 28, 28, 30, 39, 44, 40, 52, 56, 50, 56, 68, 60, 76, 70, 70, 87, 92, 80, 100, 100, 90, 97, 116, 100, 124, 112, 110, 136, 120, 120, 148, 152, 130, 140, 164, 140, 172, 154, 150, 184, 188, 160, 196, 174, 170, 182, 212, 180, 196, 189, 190, 232, 236
Offset: 1
Keywords
Examples
a(1)=2 because the only triangle with integer sides a<=b<c and inradius 1 is {3,4,5}; its middle side is 4.
a(2)=8: 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 middle sides is min(12,8,25,15,10)=8.
References
- Mohammad K. Azarian, Circumradius and Inradius, Problem S125, Math Horizons, Vol. 15, Issue 4, April 2008, p. 32. Solution published in Vol. 16, Issue 2, November 2008, p. 32.
Links
- David W. Wilson, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A120062 [triangles with integer inradius], A120252 [primitive triangles with integer inradius], A057721 [maximum of longest sides], A120063 [minimum of longest sides], A058331 [maximum of shortest sides], A082044 [maximum of middle sides], A005408 [minimum of shortest sides], A007237.
See A120062 for sequences related to integer-sided triangles with integer inradius n.
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