OFFSET
1,1
COMMENTS
Primitive solutions are in A365688.
From Jon E. Schoenfield, Sep 15 2023: (Start)
If k is a term, then so is m^2 * k for every m > 1.
Every even term is four times a smaller term.
Every odd term is the square root of the sum of one odd fourth power and two even fourth powers.
(End)
REFERENCES
Jean-Marie De Koninck, "Those Fascinating Numbers", AMS, 2008, entry 481.
EXAMPLE
1924^2 = 24^4 + 30^4 + 40^4.
PROG
(Python)
from itertools import count, islice
from sympy import integer_nthroot
def A365657_gen(startvalue=1): # generator of terms >= startvalue
for k in count(max(startvalue, 1)):
m, flag = k**2, False
for x in count(1):
if (x4:=x**4)+2>m or flag:
break
for y in range(min(x, integer_nthroot(m-x4-1, 4)[0]), 0, -1):
if (z4:=m-x4-(y4:=y**4))>y4 or flag:
break
if integer_nthroot(z4, 4)[1]:
yield k
flag = True
break
CROSSREFS
KEYWORD
nonn
AUTHOR
Jud McCranie, Sep 14 2023
STATUS
approved