OFFSET
1,1
COMMENTS
The triples (a, b, c) are displayed in increasing order of side a, and if sides a coincide then in increasing order of the side b.
In this case, the corresponding metric relation between sides is a*c + c^2 = c * (a + c) = b^2.
Equivalently, length of side common to the two angles, one being the double of the other, of a primitive integer-sided triangle.
For the corresponding primitive triples and miscellaneous properties and references, see A343063.
FORMULA
a(n) = A343063(n, 1).
EXAMPLE
According to inequalities between a, b, c, there exist 3 types of such triangles:
c < a < b for the smallest side a = 5 and triple (5, 6, 4).
The first side a for which there exist two distinct triangles with B = 2C is for a = 33 with the two other types of examples,
c < b < a with triple (33, 28, 16),
a < c < b with triple (33, 272, 256).
MAPLE
for a from 2 to 100 do
for c from 3 to floor(a^2/2) do
d := c*(a+c);
if issqr(d) and igcd(a, sqrt(d), c)=1 and abs(a-c)<sqrt(d) and sqrt(d)<a+c then print(a); end if;
end do;
end do;
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Apr 10 2021
STATUS
approved