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Search: id:A020882
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| A020882 |
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Ordered hypotenuses of primitive Pythagorean triangles. |
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71
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| 5, 13, 17, 25, 29, 37, 41, 53, 61, 65, 65, 73, 85, 85, 89, 97, 101, 109, 113, 125, 137, 145, 145, 149, 157, 169, 173, 181, 185, 185, 193, 197, 205, 205, 221, 221, 229, 233, 241, 257, 265, 265, 269, 277, 281, 289, 293, 305, 305, 313, 317, 325, 325, 337, 349, 353, 365, 365
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The largest member 'c' of the primitive Pythagorean triples (a,b,c) ordered by increasing c.
a(n) = sqrt[{(A120681(n)^2 + A120682(n)^2}/2]. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 24 2006
To find all triangle which have a given number as the difference between their two smallest sides. - Paul Curtz (bpcrtz(AT)free.fr), Aug 22 2008
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REFERENCES
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Frenicle: Methode pour trouver la solution des problemes par les exclusions.Page 25 of first 44 pages in Divers ouvrages de mathematique et de physique par Messieurs de l'Academie Royale des Sciences, in-folio, 6+518+1 pp., Paris, 1693. - Paul Curtz (bpcrtz(AT)free.fr), Aug 22 2008
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LINKS
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Hans Isdahl, Pythagoras site (in Norwegian)
Ron Knott, Pythagorean Triples and Online Calculators
E. S. Rowland, Primitive Solutions to x^2 + y^2 = z^2
M. Somos, Table of primitive Pythagorean triplets and related parameters
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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MATHEMATICA
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lst={}; amx=99; Do[For[b=a+1, b<(a^2/2), c=(a^2+b^2)^(1/2); If[c==IntegerPart[c]&&GCD[a, b, c]==1, AppendTo[lst, c]]; b=b+2], {a, 3, amx}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 07 2008]
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CROSSREFS
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Cf. A004613, A008846, A020883-A020886, A046086, A046087, A134961.
Adjacent sequences: A020879 A020880 A020881 this_sequence A020883 A020884 A020885
Sequence in context: A037046 A126887 A087445 this_sequence A081804 A004613 A008846
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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