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A383251 Short leg of the unique primitive Pythagorean triple whose inradius is A000108(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

%I A383251 #20 Jul 17 2025 16:31:30
%S A383251 3,3,5,11,29,85,265,859,2861,9725,33593,117573,416025,1485801,5348881,
%T A383251 19389691,70715341,259289581,955277401,3534526381,13128240841,
%U A383251 48932534041,182965127281,686119227301,2579808294649,9723892802905,36734706144305,139067101832009
%N A383251 Short leg of the unique primitive Pythagorean triple whose inradius is A000108(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%H A383251 Miguel-Ángel Pérez García-Ortega, <a href="/A383251/a383251.pdf">El Libro de las Ternas Pitagóricas</a>
%F A383251 a(n) = 2 * A000108(n) + 1.
%e A383251 Triangles begin:
%e A383251   n=0:      3,    4,    5;
%e A383251   n=1:      3,    4,    5;
%e A383251   n=2:      5,   12,   13;
%e A383251   n=3:     11,   60,   61;
%e A383251   ...
%e A383251 This sequences gives the first column.
%Y A383251 Cf. A000108 (inradius), A382114 (semiperimeter), A381483 (area), A386291 (long legs).
%K A383251 nonn,easy
%O A383251 0,1
%A A383251 _Miguel-Ángel Pérez García-Ortega_, Apr 20 2025