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.
This sequence is not increasing because a(7) = 9 < a(6) = 49.
If in triangle ABC, B = 2*C, then the corresponding metric relation between sides is a*c + c^2 = c * (a + c) = b^2.
All terms are perfect squares >= 4.
For the corresponding primitive triples and miscellaneous properties and references, see A343063.
FORMULA
a(n) = A343063(n, 3)
EXAMPLE
According to inequalities between a, b, c, there exist 3 types of such triangles:
c = 4 with c < a < b for the first triple (5, 6, 4).
c = 9 with c < b < a for the seventh triple (16, 15, 9).
c = 16 with a < c < b for the third triple (9, 20, 16).
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(c); end if;
end do;
end do;
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Apr 12 2021
STATUS
approved