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Search: id:A156689
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| A156689 |
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Inradii of primitive Pythagorean triples a^2+b^2=c^2, 0<a<b<c with gcd(a,b)=1, and sorted to correspond to increasing a (given in A020884). |
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1
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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REFERENCES
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Rogers, D.G.: Putting Pythagoras in the frame, Mathematics Today, The Institute of Mathematics and its Applications, Vol.44, No.3, June 2008, pp. 123-125.
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LINKS
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Ron Knott, Right-angled Triangles and Pythagoras' Theorem
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FORMULA
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A156689(n)=1/2 (A020884(n)+A156678(n)-A156679(n))
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EXAMPLE
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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.
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MATHEMATICA
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PrimitivePythagoreanTriplets[n_]:=Module[{t={{3, 4, 5}}, i=4, j=5}, While[i<n, If[GCD[i, j]==1, h=Sqrt[i^2+j^2]; If[IntegerQ[h] && j<n, AppendTo[t, {i, j, h}]]; ]; If[j<n, j+=2, i++; j=i+1]]; t]; k=30; data1=PrimitivePythagoreanTriplets[2k^2+2k+1]; data2=Select[data1, #[[1]]<=2k+1 &]; 1/2(#[[1]]+#[[2]]-#[[3]]) &/@data2
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CROSSREFS
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A020884, A020888, A156678, A156679
Sequence in context: A024811 A131138 A093878 this_sequence A004396 A131737 A066481
Adjacent sequences: A156686 A156687 A156688 this_sequence A156690 A156691 A156692
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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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