A382097 Sum of the legs of the unique primitive Pythagorean triple whose inradius is the n-th prime and whose short leg is an odd number.

17, 31, 71, 127, 287, 391, 647, 799, 1151, 1799, 2047, 2887, 3527, 3871, 4607, 5831, 7199, 7687, 9247, 10367, 10951, 12799, 14111, 16199, 19207, 20807, 21631, 23327, 24199, 25991, 32767, 34847, 38087, 39199, 44999, 46207, 49927, 53791, 56447, 60551

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 and the long leg is A367573(2,2) = 24 so the sum of the legs is then a(2) = 7 + 24 = 31.
		

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, A382070, A098996.

Programs

Mathematica

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

Formula

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

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