OFFSET
1,2
EXAMPLE
2435 is a term since 2435 + 2^5 + 4^5 + 3^5 + 5^5 = 19^3;
3403 is a term since 3403 + 3^5 + 4^5 + 0^5 + 3^5 = 17^3.
MAPLE
filter:= proc(n) local x, d;
x:= n + add(d^5, d = convert(n, base, 10));
surd(x, 3)::integer
end proc:
select(filter, [$0..10^5]); # Robert Israel, Feb 09 2021
MATHEMATICA
Select[Range[0, 500000], IntegerQ@ Power[# + Total[IntegerDigits[#]^5], 1/3] &] (* Michael De Vlieger, Feb 22 2021 *)
Select[Range[0, 416000], IntegerQ[Surd[#+Total[IntegerDigits[#]^5], 3]]&] (* Harvey P. Dale, Jul 19 2022 *)
PROG
(PARI) isok(k) = ispower(k+vecsum(apply(x->x^5, digits(k))), 3); \\ Michel Marcus, Feb 09 2021
(Python)
from sympy import integer_nthroot
def powsum(n): return sum(int(d)**5 for d in str(n))
def ok(n): return integer_nthroot(n + powsum(n), 3)[1]
def aupto(lim):
alst = []
for k in range(lim+1):
if ok(k): alst.append(k)
return alst
print(aupto(415434)) # Michael S. Branicky, Feb 22 2021
CROSSREFS
KEYWORD
base,nonn,less
AUTHOR
Will Gosnell, Feb 08 2021
EXTENSIONS
More terms from Michel Marcus, Feb 09 2021
a(1)=0 prepended by Michael S. Branicky, Feb 22 2021
STATUS
approved