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Search: id:A156686
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| A156686 |
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The ordered set of a + b - c as (a,b,c) runs through all Pythagorean triples with a<b<c. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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REFERENCES
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McCullough, Darryl; Height and Excess of Pythagorean Triples, Mathematics Magazine, Vol. 78, No. 1, February 2005.
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LINKS
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McCullough, Darryl, Height and Excess of Pythagorean Triples
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EXAMPLE
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The smallest excess in any Pythagorean triangle is 2, which occurs in (3,4,5) because 3+4-5=2. Hence a(1)=2.
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MATHEMATICA
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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
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CROSSREFS
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A020887
Sequence in context: A113724 A161794 A111650 this_sequence A085914 A014684 A113638
Adjacent sequences: A156683 A156684 A156685 this_sequence A156687 A156688 A156689
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Ant King (mathstutoring(AT)ntlworld.com), Feb 18 2009
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