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 A156687 Perimeters of Pythagorean triangles that can be constructed in exactly 5 different ways. 4
 420, 660, 924, 1008, 1080, 1200, 1512, 1584, 1716, 1800, 1872, 1890, 2700, 3150, 3168, 3240, 3480, 3528, 3570, 3720, 3744, 4410, 4440, 4536, 4590, 4704, 4872, 4896, 4950, 5208, 5292, 5472, 5600, 5670, 6000, 6090, 6210, 6216, 6624, 6630, 6660, 6888 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For any given N we can always find at least N Pythagorean triangles with the same perimeter. REFERENCES Sierpinski, W.; Pythagorean Triangles, Dover Publications, Inc., Mineola, New York, 2003. Beiler, Albert H.; Recreations In The Theory Of Numbers, Chapter XIV, The Eternal Triangle, Dover Publications Inc., New York, 1964, pp. 104-134. LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 Ron Knott, Right-angled Triangles and Pythagoras' Theorem EXAMPLE As 924 is the third smallest integer that can occur as the perimeter of exactly 5 Pythagorean triples - specifically (42,440,442), (77,420,427), (132,385,407), (198,336,390) and (231,308,385) - then a(3)=924. MATHEMATICA SetSystemOptions["ReduceOptions"->{"DiscreteSolutionBound"->100000}]; AllPerimeterTriples[n_Integer]/; n>0:=Module[{result=Reduce[Reduce[{x^2+y^2==z^2, z>y>x>0, Element[{x, y, z}, Integers], x+y+z==n}, {x, y, z}]]}, If[result===False, {}, Sort[{x, y, z}/.{ToRules[result]}]]]; Select[Range[10000], Length[AllPerimeterTriples[ # ]]==5 &] CROSSREFS Cf. A098714, A099831, A099832, A099833, A009129, A010814. Sequence in context: A189982 A070237 A305416 * A191934 A147775 A169825 Adjacent sequences: A156684 A156685 A156686 * A156688 A156689 A156690 KEYWORD easy,nice,nonn AUTHOR Ant King, Feb 18 2009 STATUS approved

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Last modified May 28 15:59 EDT 2023. Contains 363019 sequences. (Running on oeis4.)