A353342 - OEIS

%I #15 May 06 2022 19:59:58

%S 0,2,4,20,40,200,202,400,2000,2002,2020,4000,20000,20002,20020,20200,

%T 40000,200000,200002,200020,200200,202000,400000,2000000,2000002,

%U 2000020,2000200,2002000,2020000,4000000,20000000,20000002,20000020,20000200,20000202,20002000,20002002,20020000,20200000

%N Numbers k such that k and k^3 use only even digits.

%C Numbers k such that k^3 has only even digits are in A052004.

%t seq[ndigmax_] := Module[{nums = Tuples[{0, 2, 4, 6, 8}, ndigmax]}, Select[FromDigits /@ nums, AllTrue[IntegerDigits[#^3], EvenQ] &]]; seq[8] (* _Amiram Eldar_, May 06 2022 *)

%o (Python)

%o from itertools import count, islice, product

%o def agen(): # generator of terms

%o     for digits in count(1):

%o         for p in product("02468", repeat=digits):

%o             if len(p) > 1 and p[0] == "0": continue

%o             k = int("".join(p))

%o             if set(str(k**3)) <= set("02468"):

%o                 yield k

%o print(list(islice(agen(), 40))) # _Michael S. Branicky_, May 06 2022

%Y Cf. A085597 (similar, but with odd digits).

%Y Intersection of A014263 and A052004.

%K nonn,base

%O 1,2

%A _Bernard Schott_, May 06 2022