A378965 Semiperimeter of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 is A002315(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

1, 91, 3321, 114003, 3879505, 131828203, 4478506761, 152138726691, 5168245923361, 175568267678203, 5964153117476505, 202605639255558003, 6882627590483364721, 233806732489121022091, 7942546277342372594601, 269812766698916052264003, 9165691521496087693591105, 311363698964228006760021403

Offset

0,2

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=0..17.

Formula

a(n) = (A377726(n,1) + A377726(n,2) + A377726(n,3))/2.

Example

For n=2, the short leg is A377726(2,1) = 13, the long leg is A377725(2,2) = 842 and the hypotenuse is A377725(2,3) = 85 so the semiperimeter is then a(2) = (13 + 84 + 85)/2 = 91.

Mathematica

s[n_]:=s[n]=Module[{ra}, ra=((1+Sqrt[2])^(2n+1)-(Sqrt[2]-1)^(2n+1))/2; {ra(2ra-1)}]; semis={}; Do[semis=Join[semis, FullSimplify[s[n]]], {n, 0, 17}]; semis

Crossrefs

Cf. A002315, A377011, A377016, A377017, A377726, A378965.

Sequence in context: A332913 A133416 A169937 * A047697 A096054 A129965

Adjacent sequences: A378962 A378963 A378964 * A378966 A378967 A378968

Keyword

nonn,easy

Author

Miguel-Ángel Pérez García-Ortega, Dec 12 2024

Status

approved