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Search: id:A120089
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| A120089 |
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Square perimeters of primitive Pythagorean triangles. |
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+0
2
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| 144, 900, 3136, 8100, 17424, 23716, 33124, 43264, 54756, 57600, 93636, 115600, 139876, 144400, 166464, 174724, 207936, 213444, 244036, 298116, 304704, 357604, 414736, 422500, 476100, 490000, 541696, 571536, 640000, 722500, 746496, 756900
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Square entries of A024364.
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LINKS
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P.Yiu, "Primitive Pythagorean triangles with square perimeters" in 'Recreational Mathematics' Chap.6.2 pp. 50/360
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FORMULA
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a(n)=(2*u*v)^2, where u=sqrt(j/2) and v=sqrt(j+k) {for coprime pairs (j,k),j>k with odd k such that pairs (u,v),u<v are coprime with v odd}
a(n)=A024364(k)=A000290(j) for some k and j. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2006
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MAPLE
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isA024364 := proc(an) local r::integer, s::integer ; for r from floor((an/4)^(1/2)) to floor((an/2)^(1/2)) do for s from r-1 to 1 by -2 do if 2*r*(r+s) = an and gcd(r, s) < 2 then RETURN(true) ; fi ; if 2*r*(r+s) < an then break ; fi ; od ; od : RETURN(false) ; end : isA120089 := proc(an) RETURN( issqr(an) and isA024364(an)) ; end: for n from 2 to 1200 do if isA120089(n^2) then printf("%d, ", n^2) ; fi ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2006
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CROSSREFS
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Cf. A120090.
Sequence in context: A137885 A033696 A112067 this_sequence A159748 A162669 A165080
Adjacent sequences: A120086 A120087 A120088 this_sequence A120090 A120091 A120092
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 07 2006
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2006
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