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A365657
Integers k such that k^2 can be written as the sum of three positive fourth powers.
1
481, 1924, 4329, 7696, 12025, 17316, 23569, 24961, 28721, 30784, 38961, 48100, 58201, 65441, 69121, 69264, 81289, 94276, 99844, 108225, 113241, 114884, 123136, 139009, 155844, 173641, 192400, 212121, 224649, 232804, 254449, 258489, 261764, 276484, 277056, 300625, 325156
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
A365657_list = list(islice(A365657_gen(), 6)) # Chai Wah Wu, Sep 19 2023
CROSSREFS
Sequence in context: A051980 A020271 A290338 * A254896 A165384 A365688
KEYWORD
nonn
AUTHOR
Jud McCranie, Sep 14 2023
STATUS
approved