OFFSET
1,1
COMMENTS
The triples of sides (a, b, c) with a < b < c are in increasing lexicographic order. This sequence lists the b's.
For the corresponding primitive triples and miscellaneous properties and references, see A339856.
This sequence is not increasing. For example, a(11) = 77 for triple (49, 77, 121) while a(12) = 72 for triple (64, 72, 81).
Oblong numbers k*(k+1) >= 6 form a subsequence (A002378) and belong to triples of the form (k^2, k*(k+1), (k+1)^2).
LINKS
Project Euler, Problem 370: Geometric triangles.
FORMULA
a(n) = A339856 (n, 2).
EXAMPLE
a(1) = 6 only for the smallest such triangle (4, 6, 9) with 6^2 = 4*9 and a ratio q = 3/2.
a(2) = 12 only for the triangle (9, 12, 16) with 12^2 = 9*16 and a ratio q = 4/3.
MAPLE
for a from 1 to 300 do
for b from a+1 to floor((1+sqrt(5))/2 *a) do
for c from b+1 to floor((1+sqrt(5))/2 *b) do k:=a*c;
if k=b^2 and igcd(a, b, c)=1 then print(b); end if;
end do;
end do;
end do;
PROG
(PARI) lista(nn) = {my(phi = (1+sqrt(5))/2); for (a=1, nn, for (b=a+1, floor(a*phi), for (c=b+1, floor(b*phi), if ((a*c == b^2) && (gcd([a, b, c])==1), print1(b, ", "); ); ); ); ); } \\ Michel Marcus, Dec 30 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Dec 29 2020
STATUS
approved