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(n-1) as one of its legs.

3, 5, 13, 85, 157, 12325, 90733, 2449525, 28455997, 295742792965, 171480834409967437, 656310093705697045, 1616599508725767821225590944157, 4461691012090851100342993272805, 115366949386695884000892071602798585632943213, 12002377162350258332845595301471273220420939451301220405

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

Robert G. Wilson v, Table of n, a(n) for n = 0..22

Example

a(0)=3 by definition,
a(1)=5 because it is the hypotenuse of a 3-4-5 PPT,
a(2)=13 because it is the hypotenuse of a 5-12-13 PPT,
a(3)=85 because it is the hypotenuse of a 13-84-85 PPT,
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.

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

Cf. A008846, A235598.

Sequence in context: A051901 A268021 A018928 * A180313 A053630 A155012

Adjacent sequences: A239378 A239379 A239380 * A239382 A239383 A239384

Keyword

nonn

Author

Robert G. Wilson v, Mar 17 2014

Status

approved