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

1,2

Comments

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

Links

Table of n, a(n) for n=1..39.

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 *)

Prog

(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

Crossrefs

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

Intersection of A014263 and A052004.

Sequence in context: A294230 A332626 A052004 * A027741 A137697 A192380

Adjacent sequences: A353339 A353340 A353341 * A353343 A353344 A353345

Keyword

nonn,base

Author

Bernard Schott, May 06 2022

Status

approved