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%I #20 Apr 06 2021 04:44:16
%S 4,8,12,12,15,16,20,24,24,21,24,30,28,35,36,32,40,36,40,48,45,48,45,
%T 44,42,48,60,52,56,60,63,60,56,55,70,60,72,72,64,80,68,75,77,84,63,80,
%U 72,84,76,72,80,96,99,90,96,84,90,91,88,105,112,92,84,108,105,96,120
%N The middle member 'b' of the Pythagorean triples (a,b,c) ordered by increasing c.
%H Michel Marcus, <a href="/A046084/b046084.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple.</a>
%t maxHypo = 122; hypotenuseQ[n_] := For[k = 1, True, k++, p = Prime[k]; Which[Mod[p, 4] == 1 && Divisible[n, p], Return[True], p > n, Return[False]]]; hypotenuses = Select[Range[maxHypo], hypotenuseQ]; red[c_] := {a, b, c} /. {ToRules[ Reduce[0 < a <= b && a^2 + b^2 == c^2, {a, b}, Integers]]}; Sort[Flatten[red /@ hypotenuses , 1], Last[#1] < Last[#2] &][[All, 2]] (* _Jean-François Alcover_, Oct 23 2012 *)
%Y Cf. A009000, A046083.
%K nonn,look
%O 1,1
%A _Eric W. Weisstein_
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