cp's OEIS Frontend

A369497 Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = prime(n+2) and whose short leg "a" is even.

%I A369497 #27 Feb 26 2024 10:39:19
%S A369497 8,15,17,12,35,37,20,99,101,24,143,145,32,255,257,36,323,325,44,483,
%T A369497 485,56,783,785,60,899,901,72,1295,1297,80,1599,1601,84,1763,1765,92,
%U A369497 2115,2117,104,2703,2705,116,3363,3365,120,3599,3601,132,4355,4357,140,4899,4901,144,5183,5185,156,6083,6085
%N A369497 Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = prime(n+2) and whose short leg "a" is even.
%C A369497 See Exercise 3.5 of the reference.
%D A369497 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.
%H A369497 Miguel-Ángel Pérez García-Ortega, <a href="/A369497/a369497.pdf">Ejercicio 3.5</a>.
%F A369497 Row n = (a, b, c) = (2*p - 2, p^2 - 2*p, p^2 - 2*p + 2), where p = prime(n+2) = A000040(n+2).
%e A369497 Table begins:
%e A369497   n=1:   8,  15,  17;
%e A369497   n=2:  12,  35,  37;
%e A369497   n=3:  20,  99, 101;
%e A369497   n=4:  24, 143, 145;
%e A369497   n=5:  32, 255, 257;
%Y A369497 Cf. A037168 (short leg), A040976 (inradius).
%K A369497 nonn,easy,tabf
%O A369497 1,1
%A A369497 _Miguel-Ángel Pérez García-Ortega_, Jan 24 2024