A383834 Sum of the legs of the unique primitive Pythagorean triple whose inradius is A000217(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

1, 7, 31, 97, 241, 511, 967, 1681, 2737, 4231, 6271, 8977, 12481, 16927, 22471, 29281, 37537, 47431, 59167, 72961, 89041, 107647, 129031, 153457, 181201, 212551, 247807, 287281, 331297, 380191, 434311, 494017, 559681, 631687, 710431, 796321, 889777, 991231, 1101127, 1219921, 1348081

Offset: 0

Author

Miguel-Ángel Pérez García-Ortega, May 11 2025

Keywords

• nonn
• easy

Examples

			For n=1, the short leg is A002061(1) = 3 and the long leg is A212135(2) = 4 so the sum of the legs is then a(1) = 3 + 4 = 7.
		

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. A000217, A383833, A002061, A006007, A058919, A336535.

Programs

Mathematica

a=Table[(n(n+1))/2,{n,0,40}];Apply[Join,Map[{2#^2+4#+1}&,a]]

Formula

a(n) = 2*(A000217(n))^2 + 4*A000217(n) + 1.

a(n) = 6*A006007(n) + 1