A382097 - OEIS

%I #37 Mar 24 2025 02:02:53

%S 17,31,71,127,287,391,647,799,1151,1799,2047,2887,3527,3871,4607,5831,

%T 7199,7687,9247,10367,10951,12799,14111,16199,19207,20807,21631,23327,

%U 24199,25991,32767,34847,38087,39199,44999,46207,49927,53791,56447,60551

%N 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.

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

%H Miguel-Ángel Pérez García-Ortega, <a href="/A382097/a382097.pdf">El Libro de las Ternas Pitagóricas</a>

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

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

%e 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.

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

%Y Cf. A034953, A367573, A382070, A098996.

%K nonn,easy

%O 1,1

%A _Miguel-Ángel Pérez García-Ortega_, Mar 15 2025