OFFSET
1,1
COMMENTS
All rational isosceles triangles are the join of two identical rational right triangles along one of their common legs. Therefore, for any g, a squarefree congruent number, it can be the area of the right triangle creating a rational isosceles triangle with area 2g. If g is odd then the rational isosceles triangle will have squarefree k = 2g. If g is even then the rational isosceles triangle can be reduced by a factor 4 to give a squarefree value for k = g/2.
LINKS
Frank M Jackson, Table of n, a(n) for n = 1..1787
EXAMPLE
The congruent number 5 can create a rational right triangle with sides (9/6, 40/6, 41/6)) and squarefree area 5. This can create a rational isosceles triangle with sides (3, 41/6, 41/6) or (80/6, 41/6, 41/6) with squarefree area 10.
However the congruent number 6 can create a rational right triangle with sides (3, 4, 5)) and squarefree area 6. This can create a rational isosceles triangle with sides (5/2, 5/2, 3) or (4, 5/2, 5/2) with squarefree area 3.
MATHEMATICA
lst = Last /@ReadList["https://oeis.org/A006991/b006991.txt", {Number, Number}]; lst1={}; Do[If[EvenQ[lst[[n]]], AppendTo[lst1, lst[[n]]/2], AppendTo[lst1, 2 lst[[n]]]], {n, 1, Length@lst}]; (Sort@lst1)[[1 ;; 75]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Frank M Jackson, Aug 08 2024
STATUS
approved