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.
Original entry on oeis.org
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
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.
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a=Table[LucasL[n],{n,0,15}];Apply[Join,Map[{2#+1,2#^2+2#,2#^2+2#+1}&,a]]
A380823
Semiperimeter of the unique primitive Pythagorean triple whose inradius is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
Original entry on oeis.org
15, 6, 28, 45, 120, 276, 703, 1770, 4560, 11781, 30628, 79800, 208335, 544446, 1423828, 3725085, 9748320, 25514796, 66787903, 174835650, 457697640, 1198222581, 3136914028, 8212428720, 21500225295, 56288009526, 147363418828, 385801624845, 1010040449160, 2644318093956, 6922911197503
Offset: 0
For n=2, the short leg is A380821(2,1) = 7, the long leg is A380821(2,2) = 24 and the hypotenuse is A380821(2,3) = 25 so the semiperimeter is then a(2) = (7 + 24 + 25)/2 = 28.
- 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[LucasL[n],{n,0,30}];Apply[Join,Map[{(#+1)(2#+1)}&,a]]
A381721
Sum of the legs of the unique primitive Pythagorean triple whose inradius is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
Original entry on oeis.org
17, 7, 31, 49, 127, 287, 721, 1799, 4607, 11857, 30751, 79999, 208657, 544967, 1424671, 3726449, 9750527, 25518367, 66793681, 174844999, 457712767, 1198247057, 3136953631, 8212492799, 21500328977, 56288177287, 147363690271, 385802064049, 1010041159807, 2644319243807, 6922913058001, 18124414244999, 47450320478207
Offset: 0
For n=2, the short leg is A380821(2,1) = 7 and the long leg is A380821(2,2) = 24 so the semiperimeter is then a(2) = 7 + 24 = 31.
- 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[LucasL[n],{n,0,35}];Apply[Join,Map[{2#^2+4#+1}&,a]]
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