A380821 Length of the shorts leg in the unique primitive Pythagorean triple whose inradius is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
5, 3, 7, 9, 15, 23, 37, 59, 95, 153, 247, 399, 645, 1043, 1687, 2729, 4415, 7143, 11557, 18699, 30255, 48953, 79207, 128159, 207365, 335523, 542887, 878409, 1421295, 2299703, 3720997, 6020699, 9741695, 15762393, 25504087, 41266479, 66770565, 108037043
Offset: 0
Examples
n=0: 5, 12, 13; n=1: 3, 4, 5; n=2: 7, 24, 25; n=3: 9, 40, 41. This sequence is the first column.
Links
- Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
Programs
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Mathematica
a=Table[LucasL[n],{n,0,15}];Apply[Join,Map[{2#+1,2#^2+2#,2#^2+2#+1}&,a]]
Formula
a(n) = 2*A000032(n) + 1.