A383039 Sum of the legs of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000032(n) and its long leg and hypotenuse are consecutive natural numbers.

7, 1, 17, 31, 97, 241, 647, 1681, 4417, 11551, 30257, 79201, 207367, 542881, 1421297, 3720991, 9741697, 25504081, 66770567, 174807601, 457652257, 1198149151, 3136795217, 8212236481, 21499914247, 56287506241, 147362604497, 385800307231, 1010038317217, 2644314644401, 6922905616007

Offset: 0

Author

Miguel-Ángel Pérez García-Ortega, Apr 13 2025

Keywords

• nonn
• easy

Examples

			For n=3, the short leg is A382379(3,1) = 5 and the long leg is A382379(3,2) = 12 so the sum of the legs is then a(2) = 5 + 12 = 17.
		

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. A000032, A382379, A382409, A382410, A001254.

Programs

Mathematica

a=Table[LucasL[n],{n,0,30}];Apply[Join,Map[{2#^2-1}&,a]]

Formula

a(n) = A382379(n,1) + A382379(n,2).

a(n) = 2*Lucas(n)^2 - 1.

a(n) = 2*A001254(n) - 1.