A120570 Smallest perimeter of triangles with integer sides and inradius n.

12, 24, 32, 42, 60, 64, 84, 84, 96, 108, 132, 126, 156, 162, 156, 168, 204, 190, 228, 210, 220, 240, 276, 250, 300, 312, 288, 294, 348, 312, 372, 336, 352, 408, 372, 378, 444, 456, 416, 420, 492, 440, 516, 462, 468, 552, 564, 500, 588, 540, 544, 546, 636, 570

Offset: 1

Author

David W. Wilson, Jun 17 2006

Keywords

• nonn

Comments

Empirically, 6*sqrt(3) <= a(n)/n <= 12. The lower bound is provably tight.

a(n) == 0 (mod 4).

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

See A120062 for sequences related to integer-sided triangles with integer inradius n.