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

1,1

Comments

Terms a(11),..., a(100) computed by Thomas Mautsch (mautsch(AT)ethz.ch).

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

Example

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.

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.

Sequence in context: A310990 A310991 A310992 * A310993 A191330 A310994

Adjacent sequences: A120061 A120062 A120063 * A120065 A120066 A120067

Keyword

nonn

Author

Hugo Pfoertner, Jun 13 2006

Status

approved