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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.

%I A382097 #37 Mar 24 2025 02:02:53
%S A382097 17,31,71,127,287,391,647,799,1151,1799,2047,2887,3527,3871,4607,5831,
%T A382097 7199,7687,9247,10367,10951,12799,14111,16199,19207,20807,21631,23327,
%U A382097 24199,25991,32767,34847,38087,39199,44999,46207,49927,53791,56447,60551
%N 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.
%D A382097 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%H A382097 Miguel-Ángel Pérez García-Ortega, <a href="/A382097/a382097.pdf">El Libro de las Ternas Pitagóricas</a>
%F A382097 a(n) = 2*(prime(n))^2 + 4*prime(n) + 1.
%F A382097 a(n) = A367573(n,1) + A367573(n,2).
%e A382097 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 A382097 a=Table[Prime[n],{n,1,40}];Apply[Join,Map[{2#^2+4#+1}&,a]]
%Y A382097 Cf. A034953, A367573, A382070, A098996.
%K A382097 nonn,easy
%O A382097 1,1
%A A382097 _Miguel-Ángel Pérez García-Ortega_, Mar 15 2025