A377725 Table read by rows: row n is the unique primitive Pythagorean triple whose inradius is A002315(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

3, 4, 5, 15, 112, 113, 83, 3444, 3445, 479, 114720, 114721, 2787, 3883684, 3883685, 16239, 131852560, 131852561, 94643, 4478648724, 4478648725, 551615, 152139554112, 152139554113, 3215043, 5168250745924, 5168250745925, 18738639, 175568295786160, 175568295786161

Offset

1,1

References

Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.

Links

Table of n, a(n) for n=1..30.

Formula

row(n) = (2*A002315(n) + 1, 2*A002315(n)(A002315(n) + 1), 2*A002315(n)(A002315(n) + 1) + 1).

Example

 n=1:      3,         4,         5;
 n=2:     15,       112,       113;
 n=3:     83,      3444,      3445;
 n=4:    479,    114720,    114721;

Mathematica

r[n_]:=r[n]=Module[{r}, r=((1+Sqrt[2])^(2n+1)-(Sqrt[2]-1)^(2n+1))/2; {2r+1, 2r^2+2r, 2r^2+2r+1}]; inradio={}; Do[inradio=Join[inradio, FullSimplify[r[n]]], {n, 0, 10}]; inradio

Crossrefs

Cf. A002315, A377011, A377016, A377017, A377726.

Sequence in context: A347391 A051033 A346601 * A242787 A031199 A173027

Adjacent sequences: A377722 A377723 A377724 * A377726 A377727 A377728

Keyword

nonn,easy,tabf

Author

Miguel-Ángel Pérez García-Ortega, Nov 05 2024

Status

approved