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Search: id:A008846
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| A008846 |
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Hypotenuses of primitive Pythagorean triangles. |
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+0
21
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| 5, 13, 17, 25, 29, 37, 41, 53, 61, 65, 73, 85, 89, 97, 101, 109, 113, 125, 137, 145, 149, 157, 169, 173, 181, 185, 193, 197, 205, 221, 229, 233, 241, 257, 265, 269, 277, 281, 289, 293, 305, 313, 317, 325, 337, 349, 353, 365, 373, 377, 389, 397, 401, 409, 421, 425, 433
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Sequence includes all entries of A002144
n for which there is no solution to 4/n = 2/x + 1/y for integers y > x > 0. Related to A073101. - T. D. Noe (noe(AT)sspectra.com), Sep 30 2002
Discovered by Frenicle (on Pythagorean triangles) : Methode pour trouver .., page 14 on 44. First text of Divers ouvrages .. Par Messieurs de l'Academie Royale des Sciences,in-folio,6+518+1pp,Paris,1693. Also A020882 with only one of doubled terms (first:65). [From Paul Curtz (bpcrtz(AT)free.fr), Sep 03 2008]
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, pp. 10, 107.
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LINKS
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Ron Knott, Pythagorean Triples and Online Calculators
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FORMULA
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x^2+y^2 where x is even, y is odd and gcd(x, y)=1. Essentially the same as A004613.
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MAPLE
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for x from 1 by 2 to 50 do for y from 2 by 2 to 50 do if gcd(x, y) = 1 then print(x^2+y^2); fi; od; od; [ then sort ].
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MATHEMATICA
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Union[ Map[ Plus@@(#1^2)&, Select[ Flatten[ Array[ {2*#1, 2*#2-1}&, {10, 10} ], 1 ], GCD@@#1 == 1& ] ] ] - Olivier Gerard, Aug 15 1997
lst = {}; Do[ If[ GCD[m, n] == 1, a = 2 m*n; b = m^2 - n^2; c = m^2 + n^2; AppendTo[lst, c]], {m, 100}, {n, If[ OddQ@m, 2, 1], m - 1, 2}]; Take[ Union@ lst, 57] [From Robert G. Wilson v (rgwv(AT)rgwv.com), May 02 2009]
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CROSSREFS
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Cf. A020882, A073101.
Sequence in context: A020882 A081804 A004613 this_sequence A162597 A120960 A094194
Adjacent sequences: A008843 A008844 A008845 this_sequence A008847 A008848 A008849
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Ralph Peterson (RALPHP(AT)LIBRARY.nrl.navy.mil)
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Sep 30 2002
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