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

Author

Bernard Schott, Jan 05 2022

Keywords

• nonn
• base

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

Examples

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• International Mathematical Talent Search, Problem 1/2, Round 2.

Crossrefs

Cf. A061807, A350536.

Terms belong to A014263.

Programs

Mathematica

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

PARI

a(n) = my(k=2); while(#select(x->((x%2) == 1), digits(k*n)), k++); k*n; \\ Michel Marcus, Jan 12 2022

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

Extensions

More terms from Michael S. Branicky, Jan 05 2022