A382379
Length of the long leg in the unique primitive Pythagorean triple (x,y,z) such that (x-y+z)/2 is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
Original entry on oeis.org
4, 0, 12, 24, 84, 220, 612, 1624, 4324, 11400, 30012, 78804, 206724, 541840, 1419612, 3718264, 9737284, 25496940, 66759012, 174788904, 457622004, 1198100200, 3136716012, 8212108324, 21499706884, 56287170720, 147362061612, 385799428824, 1010036895924
Offset: 0
The triangles begin:
n=0: 3, 4, 5;
n=1: 1, 0, 1;
n=2: 5, 12, 13;
n=3: 7, 24, 25;
...
This sequence gives the middle column
A382409
Semiperimeter of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
Original entry on oeis.org
6, 1, 15, 28, 91, 231, 630, 1653, 4371, 11476, 30135, 79003, 207046, 542361, 1420455, 3719628, 9739491, 25500511, 66764790, 174798253, 457637131, 1198124676, 3136755615, 8212172403, 21499810566, 56287338481, 147362333055, 385799868028, 1010037606571, 2644313494551, 6922903755510
Offset: 0
For n=3, the short leg is A382379(2,1) = 5, the long leg is A382379(2,2) = 12 and the hypotenuse is A382379(2,3) = 13 so the semiperimeter is then a(3) = (5 + 12 + 13)/2 = 15.
- Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
-
a=Table[LucasL[n],{n,0,30}];Apply[Join,Map[{#(2#-1)}&,a]]
A383039
Sum of the legs of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000032(n) and its long leg and hypotenuse are consecutive natural numbers.
Original entry on oeis.org
7, 1, 17, 31, 97, 241, 647, 1681, 4417, 11551, 30257, 79201, 207367, 542881, 1421297, 3720991, 9741697, 25504081, 66770567, 174807601, 457652257, 1198149151, 3136795217, 8212236481, 21499914247, 56287506241, 147362604497, 385800307231, 1010038317217, 2644314644401, 6922905616007
Offset: 0
For n=3, the short leg is A382379(3,1) = 5 and the long leg is A382379(3,2) = 12 so the sum of the legs is then a(2) = 5 + 12 = 17.
- Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
-
a=Table[LucasL[n],{n,0,30}];Apply[Join,Map[{2#^2-1}&,a]]
Showing 1-3 of 3 results.