OFFSET
1,2
COMMENTS
Since A055013(k) < 9^4*(1+log_10(k)) and k^2 + 9^4*(1+log_10(k^2)) < (k+1)^2 for k > 32918, one need only search up to k = 32918.
EXAMPLE
a(3) = 137 is a term because 137^2 = 18769 and 18769 + 1^4 + 8^4 + 7^4 + 6^4 + 9^4 = 182^2.
MAPLE
select(n -> issqr(n^2 + add(t^4, t = convert(n^2, base, 10))), [$0..32918]);
PROG
(Python)
from math import isqrt
def sq(n): return isqrt(n)**2 == n
def ok(n): return sq(n**2 + sum(int(d)**4 for d in str(n**2)))
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Feb 12 2023
CROSSREFS
KEYWORD
nonn,bref,fini,full,base
AUTHOR
Robert Israel and Will Gosnell, Feb 06 2023
STATUS
approved