A382608
Long leg of the unique primitive Pythagorean triple whose inradius is A000045(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
Original entry on oeis.org
4, 4, 12, 24, 60, 144, 364, 924, 2380, 6160, 16020, 41760, 109044, 285012, 745420, 1950312, 5104012, 13359280, 34969884, 91543980, 239651724, 627394464, 1642504612, 4300075584, 11257651300, 29472763684, 77160454284, 202008299064, 528863957340, 1384582787280
Offset: 1
Triangle begins:
n=1: 3, 4, 5;
n=2: 3, 4, 5;
n=3: 5, 12, 13;
where this sequence is the middle column.
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a=Table[Fibonacci[n],{n,0,16}];Apply[Join,Map[{2#+1,2#^2+2#,2#^2+2#+1}&,a]]
A382609
Semiperimeter of the unique primitive Pythagorean triple whose inradius is A000045(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
Original entry on oeis.org
1, 6, 6, 15, 28, 66, 153, 378, 946, 2415, 6216, 16110, 41905, 109278, 285390, 746031, 1951300, 5105610, 13361865, 34974066, 91550746, 239662671, 627412176, 1642533270, 4300121953, 11257726326, 29472885078, 77160650703, 202008616876, 528864471570, 1384583619321
Offset: 0
For n=2, the short leg is A382608(2,1) = 3, the long leg is A382608(2,2) = 4 and the hypotenuse is A382608(2,3) = 5 so the semiperimeter is then a(2) = (3 + 4 + 5)/2 = 6.
- Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
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a=Table[Fibonacci[n],{n,0,30}];Apply[Join,Map[{(#+1)(2#+1)}&,a]]
A382308
Sum of the legs of the unique primitive Pythagorean triple whose inradius is A000045(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
Original entry on oeis.org
1, 7, 7, 17, 31, 71, 161, 391, 967, 2449, 6271, 16199, 42049, 109511, 285767, 746641, 1952287, 5107207, 13364449, 34978247, 91557511, 239673617, 627429887, 1642561927, 4300168321, 11257801351, 29473006471, 77160847121, 202008934687, 528864985799, 1384584451361
Offset: 0
For n=2, the short leg is A382608(2,1) = 3 and the long leg is A382608(2,2) = 4 so the sum of the legs is then a(2) = 3 + 4 = 7.
- Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
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a=Table[Fibonacci[n],{n,0,30}];Apply[Join,Map[{2#^2+4#+1}&,a]]
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