A046084 The middle member 'b' of the Pythagorean triples (a,b,c) ordered by increasing c.
4, 8, 12, 12, 15, 16, 20, 24, 24, 21, 24, 30, 28, 35, 36, 32, 40, 36, 40, 48, 45, 48, 45, 44, 42, 48, 60, 52, 56, 60, 63, 60, 56, 55, 70, 60, 72, 72, 64, 80, 68, 75, 77, 84, 63, 80, 72, 84, 76, 72, 80, 96, 99, 90, 96, 84, 90, 91, 88, 105, 112, 92, 84, 108, 105, 96, 120
Offset: 1
Links
- Michel Marcus, Table of n, a(n) for n = 1..10000
- Eric Weisstein's World of Mathematics, Pythagorean Triple.
Programs
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Mathematica
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 *)