A350538 a(n) is the smallest proper multiple of n which contains only even digits.

2, 4, 6, 8, 20, 24, 28, 24, 288, 20, 22, 24, 26, 28, 60, 48, 68, 288, 228, 40, 42, 44, 46, 48, 200, 208, 486, 84, 406, 60, 62, 64, 66, 68, 280, 288, 222, 228, 468, 80, 82, 84, 86, 88, 2880, 460, 282, 240, 686, 200, 204, 208, 424, 486, 220, 224, 228, 406, 826

Offset

1,1

Comments

Inspired by the problem 1/2 of International Mathematical Talent Search, round 2 (see link).

Differs from A061807 when n is in A014263. - Michel Marcus, Jan 05 2022

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

International Mathematical Talent Search, Problem 1/2, Round 2.

Example

a(9) = 288 = 32 * 9 is the smallest multiple of 9 which contains only even digits.

Mathematica

a[n_] := Module[{k = 2*n}, While[! AllTrue[IntegerDigits[k], EvenQ], k += n]; k]; Array[a, 60] (* Amiram Eldar, Jan 05 2022 *)

Prog

(Python)
def a(n):
    m, inc = 2*n, n if n%2 == 0 else 2*n
    while not set(str(m)) <= set("02468"): m += inc
    return m
print([a(n) for n in range(1, 60)]) # Michael S. Branicky, Jan 05 2022
(Python)
from itertools import count, product
def A350538(n):
    for l in count(len(str(n))-1):
        for a in '2468':
            for b in product('02468', repeat=l):
                k = int(a+''.join(b))
                if k > n and k % n == 0:
                    return k # Chai Wah Wu, Jan 12 2022
(PARI) a(n) = my(k=2); while(#select(x->((x%2) == 1), digits(k*n)), k++); k*n; \\ Michel Marcus, Jan 12 2022

Crossrefs

Cf. A061807, A350536.

Terms belong to A014263.

Sequence in context: A169906 A251853 A061651 * A131122 A335209 A119261

Adjacent sequences: A350535 A350536 A350537 * A350539 A350540 A350541

Keyword

nonn,base

Author

Bernard Schott, Jan 05 2022

Extensions

More terms from Michael S. Branicky, Jan 05 2022

Status

approved