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.
3, 4, 5, 11, 60, 61, 23, 264, 265, 39, 760, 761, 59, 1740, 1741, 83, 3444, 3445, 111, 6160, 6161, 143, 10224, 10225, 179, 16020, 16021, 219, 23980, 23981, 263, 34584, 34585, 311, 48360, 48361, 363, 65884, 65885, 419, 87780, 87781, 479, 114720, 114721, 543, 147424, 147425
Offset: 1
Examples
n=1: 3, 4, 5; n=2: 11, 60, 61; n=3: 23, 264, 265; ...
Links
- José Miguel Blanco Casado and Miguel-Ángel Pérez García-Ortega, El Libro de las Ternas Pitagóricas
Programs
-
Mathematica
a=Table[(n(n+1)),{n,1,16}];Apply[Join,Map[{2#-1,2#^2-2#,2#^2-2#+1}&,a]]
Formula
row(n) = (2*T(n) - 1, 2*T(n)*(T(n) - 1), 2*T(n)*(T(n) - 1) + 1) where T(n) = A002378(n).