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%I #12 Apr 01 2014 10:34:35
%S 3,5,13,85,157,12325,90733,2449525,28455997,295742792965,
%T 171480834409967437,656310093705697045,
%U 1616599508725767821225590944157,4461691012090851100342993272805,115366949386695884000892071602798585632943213,12002377162350258332845595301471273220420939451301220405
%N a(0) = 3, the least length of a Primitive Pythagorean Triangle (PPT). a(n) is the least hypotenuse of a PPT which has a(n-1) as one of its legs.
%C a(0)=3 because A042965(3)=3 with comments.
%C If we relax the Primitive restriction, i.e., GCD(x,y,z) can exceed 1, then we have A018928.
%H Robert G. Wilson v, <a href="/A239381/b239381.txt">Table of n, a(n) for n = 0..22</a>
%e a(0)=3 by definition,
%e a(1)=5 because it is the hypotenuse of a 3-4-5 PPT,
%e a(2)=13 because it is the hypotenuse of a 5-12-13 PPT,
%e a(3)=85 because it is the hypotenuse of a 13-84-85 PPT,
%e a(4)=157 because it is the hypotenuse of a 85-132-157 PPT, 85 is also the leg of a 85-3612-3613 PPT but its hypotenuse is larger, etc.
%t f[s_List] := Block[{x = s[[-1]]}, Append[s, Transpose[ Solve[x^2 + y^2 == z^2 && GCD[x, y, z] == 1 && y > 0 && z > 0, {y, z}, Integers]][[-1, 1, 2]]]]; lst = Nest[f, {3}, 15]
%Y Cf. A008846, A235598.
%K nonn
%O 0,1
%A _Robert G. Wilson v_, Mar 17 2014
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