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A382114

Semiperimeter of the unique primitive Pythagorean triple whose inradius is A000108(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

6, 6, 15, 66, 435, 3655, 35245, 369370, 4094091, 47292675, 564261621, 6911763951, 86538608325, 1103803048701, 14305266650521, 187980068232586, 2500329761730811, 33615543537222571, 456277456908296101, 6246438370759741771, 86175353796214314061, 1197196443861278161861, 16738118900567747790121, 235379797036403711485951

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

REFERENCES

Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.

LINKS

Table of n, a(n) for n=0..23.

Miguel-Ángel Pérez García-Ortega, El Libro de las Ternas Pitagóricas

FORMULA

a(n) = (A383251(n,1) + A383251(n,2) + A383251(n,3))/2.

a(n) = (A000108(n) + 1)*(2*A000108(n) + 1).

EXAMPLE

For n=2, the short leg is A383251(2,1) = 3, the long leg is A383251(2,2) = 4 and the hypotenuse is A383251(2,3) = 5 so the semiperimeter is then a(2) = (3 + 4 + 5)/2 = 6.

MATHEMATICA

a=Table[(2n)!/(n!(n+1)!), {n, 0, 23}]; Apply[Join, Map[{(#+1)(2#+1)}&, a]]

CROSSREFS

Cf. A000108, A383251, A381483.

Sequence in context: A382609 A257372 A058563 * A175561 A341202 A315810

Adjacent sequences: A382111 A382112 A382113 * A382115 A382116 A382117

KEYWORD

nonn,easy

AUTHOR

Miguel-Ángel Pérez García-Ortega, Apr 22 2025

STATUS

approved

URL: https://oeis.org/A382114

⇱ A382114 - OEIS