|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
easy,nice,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|