A085597 -id:A085597 - cp's OEIS frontend

A182211 The number of integers k < 10^n such that both k and k^3 mod 10^n have all odd decimal digits.

5, 25, 62, 151, 381, 833, 2163, 5291, 13317, 33519, 85179, 213083, 539212, 1344272, 3358571

Offset: 1

Victor S. Miller, Apr 18 2012

Inspired by a discussion on the math-fun list on April 18, 2012 by James R. Buddenhagen.

Cf. A085597 (n such that both n and n^3 have all odd digits).

oddDigits 0 = True
oddDigits n = let (q,r) = quotRem n 10
              in (odd r) && oddDigits q
oddSet 0 = []
oddSet 1 = [1,3..9]
oddSet k = [n | i <- [1,3..9], x <- oddSet (k-1), let n = i*10^(k-1) + x,
               oddDigits((n^3) `mod` 10^k)]
main = putStrLn $ map (length . oddSet) [1..]

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

Original entry on oeis.org

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

Bernard Schott, May 06 2022

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

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

Intersection of A014263 and A052004.

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 *)

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

cp's OEIS Frontend

A182211 The number of integers k < 10^n such that both k and k^3 mod 10^n have all odd decimal digits.

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