

A239381


a(0) = 3, the least length of a Primitive Pythagorean Triangle (PPT). a(n) is the least hypotenuse of a PPT which has a(n1) as one of its legs.


3



3, 5, 13, 85, 157, 12325, 90733, 2449525, 28455997, 295742792965, 171480834409967437, 656310093705697045, 1616599508725767821225590944157, 4461691012090851100342993272805, 115366949386695884000892071602798585632943213, 12002377162350258332845595301471273220420939451301220405
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

a(0)=3 because A042965(3)=3 with comments.
If we relax the Primitive restriction, i.e., GCD(x,y,z) can exceed 1, then we have A018928.


LINKS



EXAMPLE

a(0)=3 by definition,
a(1)=5 because it is the hypotenuse of a 345 PPT,
a(2)=13 because it is the hypotenuse of a 51213 PPT,
a(3)=85 because it is the hypotenuse of a 138485 PPT,
a(4)=157 because it is the hypotenuse of a 85132157 PPT, 85 is also the leg of a 8536123613 PPT but its hypotenuse is larger, etc.


MATHEMATICA

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]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



