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A385022 Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A002378(n) and its long leg and hypotenuse are consecutive natural numbers.

%I A385022 #20 Jul 13 2025 17:25:02
%S A385022 3,4,5,11,60,61,23,264,265,39,760,761,59,1740,1741,83,3444,3445,111,
%T A385022 6160,6161,143,10224,10225,179,16020,16021,219,23980,23981,263,34584,
%U A385022 34585,311,48360,48361,363,65884,65885,419,87780,87781,479,114720,114721,543,147424,147425
%N A385022 Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A002378(n) and its long leg and hypotenuse are consecutive natural numbers.
%H A385022 José Miguel Blanco Casado and Miguel-Ángel Pérez García-Ortega, <a href="/A383834/a383834.pdf">El Libro de las Ternas Pitagóricas</a>
%F A385022 row(n) = (2*T(n) - 1, 2*T(n)*(T(n) - 1), 2*T(n)*(T(n) - 1) + 1) where T(n) = A002378(n).
%e A385022   n=1:      3,     4,     5;
%e A385022   n=2:     11,    60,    61;
%e A385022   n=3:     23,   264,   265;
%e A385022   ...
%t A385022 a=Table[(n(n+1)),{n,1,16}];Apply[Join,Map[{2#-1,2#^2-2#,2#^2-2#+1}&,a]]
%Y A385022 Cf. A002378, A142463 (short leg), A385187 (area).
%K A385022 sign,easy,tabf
%O A385022 1,1
%A A385022 _Miguel-Ángel Pérez García-Ortega_, Jun 15 2025