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A377725 Length of the short leg of the unique primitive Pythagorean triple whose inradius is A002315(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

%I A377725 #18 Jul 13 2025 21:52:47
%S A377725 3,15,83,479,2787,16239,94643,551615,3215043,18738639,109216787,
%T A377725 636562079,3710155683,21624372015,126036076403,734592086399,
%U A377725 4281516441987,24954506565519,145445522951123,847718631141215,4940866263896163,28797478952235759,167844007449518387
%N A377725 Length of the short leg of the unique primitive Pythagorean triple whose inradius is A002315(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%H A377725 Miguel-Ángel Pérez García-Ortega, <a href="/A365577/a365577.pdf">Capitulo 5. Catetos</a>, El Libro de las Ternas Pitagóricas.
%F A377725 a(n) = 2*A002315(n) + 1.
%e A377725 Triangles begin:
%e A377725   n=1:      3,         4,         5;
%e A377725   n=2:     15,       112,       113;
%e A377725   n=3:     83,      3444,      3445;
%e A377725   n=4:    479,    114720,    114721;
%e A377725   ...
%e A377725 This sequence gives the first column.
%Y A377725 Cf. A002315, A377016, A377017, A377726, A385977 (long leg).
%K A377725 nonn,easy
%O A377725 1,1
%A A377725 _Miguel-Ángel Pérez García-Ortega_, Nov 05 2024