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A106499
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Ordered perimeter of primitive integer-sided triangle one of whose angles is twice another.
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12
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15, 28, 40, 45, 66, 77, 84, 91, 104, 120, 126, 144, 153, 170, 187, 190, 198, 209, 220, 228, 231, 260, 273, 276, 286, 299, 312, 322, 325, 345, 350, 378, 390, 400, 420, 432, 435, 442, 459, 464, 476, 493, 496, 510, 522, 527, 544, 551, 558, 561, 570, 589, 608
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OFFSET
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1,1
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COMMENTS
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The sides of the primitive triangle are given by the triple (r*s,s^2 - r^2,r^2).
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LINKS
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FORMULA
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a(n)=s*(r+s), where r<s<2r and (r, s)=1.
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MATHEMATICA
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s[p_] := Solve[1 < r < s < 2r && p == r s + s^2 && GCD[r, s] == 1, {r, s}, Integers];
Reap[For[p = 1, p <= 10000, p++, sp = s[p]; If[sp =!= {}, Sow[p]; Print[p, " ", {r s, s^2 - r^2, r^2} /. sp[[1]]]]]][[2, 1]] (* Jean-François Alcover, Mar 06 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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