A156686 The ordered set of a + b - c as (a,b,c) runs through all Pythagorean triples with a

2, 4, 4, 6, 6, 6, 8, 8, 8, 10, 10, 10, 12, 12, 12, 12, 12, 12, 14, 14, 14, 16, 16, 16, 16, 18, 18, 18, 18, 18, 20, 20, 20, 20, 20, 20, 22, 22, 22, 24, 24, 24, 24, 24, 24, 24, 24, 24, 26, 26, 26, 28, 28, 28, 28, 28, 28, 30, 30, 30, 30, 30, 30, 30, 30, 30

Offset: 1

Author

Ant King, Feb 18 2009

Keywords

• easy
• nice
• nonn

Comments

Also called the excess of a Pythagorean triangle, and is equal to the diameter of its incircle. All members of this sequence are even, and the corresponding sequence for primitive triangles only is A020887.

Examples

			The smallest excess in any Pythagorean triangle is 2, which occurs in (3,4,5) because 3+4-5=2. Hence a(1)=2.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000
• Darryl McCullough, Height and Excess of Pythagorean Triples
• Darryl McCullough, Height and Excess of Pythagorean Triples, Mathematics Magazine, Vol. 78, No. 1, February 2005.

Crossrefs

Cf. A020887.

Programs

Mathematica

data1=Reduce[ a^2+b^2==c^2 && a+b-c==# && 0