A353342 Numbers k such that k and k^3 use only even digits.

0, 2, 4, 20, 40, 200, 202, 400, 2000, 2002, 2020, 4000, 20000, 20002, 20020, 20200, 40000, 200000, 200002, 200020, 200200, 202000, 400000, 2000000, 2000002, 2000020, 2000200, 2002000, 2020000, 4000000, 20000000, 20000002, 20000020, 20000200, 20000202, 20002000, 20002002, 20020000, 20200000

Offset: 1

Author

Bernard Schott, May 06 2022

Keywords

• nonn
• base

Comments

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

Crossrefs

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

Intersection of A014263 and A052004.

Programs

Mathematica

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 *)

Python

from itertools import count, islice, product
def agen(): # generator of terms
    for digits in count(1):
        for p in product("02468", repeat=digits):
            if len(p) > 1 and p[0] == "0": continue
            k = int("".join(p))
            if set(str(k**3)) <= set("02468"):
                yield k
print(list(islice(agen(), 40))) # Michael S. Branicky, May 06 2022