A382070 Semiperimeter of the unique primitive Pythagorean triple whose inradius is the n-th prime and whose short leg is an odd number.

15, 28, 66, 120, 276, 378, 630, 780, 1128, 1770, 2016, 2850, 3486, 3828, 4560, 5778, 7140, 7626, 9180, 10296, 10878, 12720, 14028, 16110, 19110, 20706, 21528, 23220, 24090, 25878, 32640, 34716, 37950, 39060, 44850, 46056, 49770, 53628, 56280, 60378

Offset: 1

Author

Miguel-Ángel Pérez García-Ortega, Mar 15 2025

Keywords

• nonn
• easy

Examples

			For n=2, the short leg is A367573(2,1) = 7, the long leg is A367573(2,2) = 24 and the hypotenuse is A367573(2,3) = 25 so the semiperimeter is then a(2) = (7 + 24 + 25)/2 = 28.
		

References

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

Links

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

Crossrefs

Cf. A034953, A367573, A382097, A098996.

Programs

Mathematica

a=Table[Prime[n],{n,1,40}];Apply[Join,Map[{(#+1)(2#+1)}&,a]]

Formula

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

a(n) = (A367573(n,1) + A367573(n,2) + A367573(n,3))/2.