OFFSET
1,6
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10002
Yasuaki Gyoda, Positive integer solutions to (x+y)^2+(y+z)^2+(z+x)^2=12xyz, arXiv:2109.09639 [math.NT], 2021.
EXAMPLE
The array of triples begins:
( 1, 1, 1),
( 1, 1, 3),
( 1, 3, 13),
( 1, 13, 61),
( 3, 13, 217),
( 1, 61, 291),
( 1, 291, 1393),
( 3, 217, 3673),
(13, 61, 4683),
( 1, 1393, 6673),
(13, 217, 16693),
...
PROG
(PARI) N=5000;
for(k=1, N, for(j=1, k, for(i=1, j, if(i*j>k, break); if((i+j)^2+(j+k)^2+(k+i)^2==12*i*j*k, print1(i, ", ", j, ", ", k, ", ")))));
(Python)
from math import isqrt
from itertools import count, islice
def A351372_gen(): # generator of terms
for z in count(1):
z2 = z**2
for y in range(1, z+1):
a = isqrt(d := 3*y**2*(12*z2 - 4*z - 1) - 3*z2*(4*y + 1) - 2*y*z)
if a**2 == d:
x, r = divmod(12*y*z - 2*y - 2*z - 2*a, 4)
if y <= x <= z and r == 0:
yield from (y, x, z)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Seiichi Manyama, Feb 15 2022
EXTENSIONS
More terms from Chai Wah Wu, Feb 16 2022
STATUS
approved