A156689 Inradii of primitive Pythagorean triples a^2+b^2=c^2, 0A020884).

1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 6, 9, 10, 11, 11, 12, 13, 10, 13, 14, 15, 15, 12, 16, 17, 14, 17, 18, 15, 19, 19, 20, 21, 18, 21, 22, 23, 15, 23, 24, 21, 25, 22, 25, 26, 27, 27, 24, 28, 29, 21, 26, 29, 30

Offset: 1

Author

Ant King, Feb 18 2009

Keywords

• easy
• nice
• nonn

Comments

The inradius is given by r=1/2 (a+b-c)=ab/(a+b+c)=area/semiperimeter, and the inradii ordered by increasing r are in A020888.

Examples

			The eighth primitive Pythagorean triple ordered by increasing a is (13,84,85). As this has inradius 1/2 (13+84-85)=6, we have a(8)=6.
		

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.
• D. G. Rogers, Putting Pythagoras in the frame, Mathematics Today, The Institute of Mathematics and its Applications, Vol. 44, No. 3, June 2008, pp. 123-125.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Ron Knott, Right-angled Triangles and Pythagoras' Theorem

Crossrefs

Cf. A020884, A020888, A156678, A156679.

Cf. A037213.

Programs

Haskell

a156689 n = a156689_list !! (n-1)
a156689_list = f 1 1 where
   f u v | v > uu `div` 2        = f (u + 1) (u + 2)
         | gcd u v > 1 || w == 0 = f u (v + 2)
         | otherwise             = (u + v - w) `div` 2 : f u (v + 2)
         where uu = u ^ 2; w = a037213 (uu + v ^ 2)
-- Reinhard Zumkeller, Nov 09 2012

Mathematica

PrimitivePythagoreanTriplets[n_]:=Module[{t={{3,4,5}},i=4,j=5},While[i
				

Formula

A156689(n)=1/2 (A020884(n)+A156678(n)-A156679(n))