A046083 The smallest member 'a' of the Pythagorean triples (a,b,c) ordered by increasing c.

3, 6, 5, 9, 8, 12, 15, 7, 10, 20, 18, 16, 21, 12, 15, 24, 9, 27, 30, 14, 24, 20, 28, 33, 40, 36, 11, 39, 33, 25, 16, 32, 42, 48, 24, 45, 21, 30, 48, 18, 51, 40, 36, 13, 60, 39, 54, 35, 57, 65, 60, 28, 20, 48, 40, 63, 56, 60, 66, 36, 15, 69, 80, 45, 56, 72, 22, 27, 75, 44, 35

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pythagorean Triple.

Crossrefs

Cf. A046084, A009000.

Programs

Mathematica

maxHypo = 125; 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, 1]] (* Jean-François Alcover, Oct 23 2012 *)