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Search: id:A024364
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| A024364 |
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Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, A <= B); sequence gives perimeters A+B+C. |
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20
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| 12, 30, 40, 56, 70, 84, 90, 126, 132, 144, 154, 176, 182, 198, 208, 220, 234, 240, 260, 286, 306, 312, 330, 340, 374, 380, 390, 408, 418, 420, 442, 456, 462, 476, 494, 510, 532, 544, 546, 552, 570, 598, 608, 644, 646, 650, 672, 684, 690, 700
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Perimeters of primitive Pythagorean triples in increasing order.
n is in this sequence iff A070109(n)>0. This is a subset of A010814.
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LINKS
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Ron Knott, Pythagorean Triples and Online Calculators
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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 : for n from 2 to 400 do if isA024364(n) then printf("%d, ", n) ; fi ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2006
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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, p=a+b+c; AppendTo[lst, p]]; b=b+2], {a, 3, amx}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 08 2008]
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CROSSREFS
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a(n)=2*A020886(n) (with different offset).
Sequence in context: A115912 A083096 A145469 this_sequence A093507 A145470 A108278
Adjacent sequences: A024361 A024362 A024363 this_sequence A024365 A024366 A024367
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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