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A156686
The ordered set of a + b - c as (a,b,c) runs through all Pythagorean triples with a<b<c.
1
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
1,1
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.
LINKS
Darryl McCullough, Height and Excess of Pythagorean Triples, Mathematics Magazine, Vol. 78, No. 1, February 2005.
EXAMPLE
The smallest excess in any Pythagorean triangle is 2, which occurs in (3,4,5) because 3+4-5=2. Hence a(1)=2.
MATHEMATICA
data1=Reduce[ a^2+b^2==c^2 && a+b-c==# && 0<a<b<c, {a, b, c}, Integers]&/@Range[30]; DeleteCases[Table[If[Head[data1[[k]]]===Symbol, 0, If[Head[data1[[k]]]===And, k, Table[k, {i, 1, Length[data1[[k]]]}]]], {k, 1, Length[data1]}], 0]//Flatten
CROSSREFS
Cf. A020887.
Sequence in context: A113724 A161794 A111650 * A210466 A085914 A211390
KEYWORD
easy,nice,nonn
AUTHOR
Ant King, Feb 18 2009
STATUS
approved