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

%I A350538 #27 Jan 12 2022 21:00:25
%S A350538 2,4,6,8,20,24,28,24,288,20,22,24,26,28,60,48,68,288,228,40,42,44,46,
%T A350538 48,200,208,486,84,406,60,62,64,66,68,280,288,222,228,468,80,82,84,86,
%U A350538 88,2880,460,282,240,686,200,204,208,424,486,220,224,228,406,826
%N A350538 a(n) is the smallest proper multiple of n which contains only even digits.
%C A350538 Inspired by the problem 1/2 of International Mathematical Talent Search, round 2 (see link).
%C A350538 Differs from A061807 when n is in A014263. - _Michel Marcus_, Jan 05 2022
%H A350538 Chai Wah Wu, <a href="/A350538/b350538.txt">Table of n, a(n) for n = 1..10000</a>
%H A350538 International Mathematical Talent Search, <a href="https://www2.cms.math.ca/Competitions/IMTS/imts2.html">Problem 1/2</a>, Round 2.
%e A350538 a(9) = 288 = 32 * 9 is the smallest multiple of 9 which contains only even digits.
%t A350538 a[n_] := Module[{k = 2*n}, While[! AllTrue[IntegerDigits[k], EvenQ], k += n]; k]; Array[a, 60] (* _Amiram Eldar_, Jan 05 2022 *)
%o A350538 (Python)
%o A350538 def a(n):
%o A350538     m, inc = 2*n, n if n%2 == 0 else 2*n
%o A350538     while not set(str(m)) <= set("02468"): m += inc
%o A350538     return m
%o A350538 print([a(n) for n in range(1, 60)]) # _Michael S. Branicky_, Jan 05 2022
%o A350538 (Python)
%o A350538 from itertools import count, product
%o A350538 def A350538(n):
%o A350538     for l in count(len(str(n))-1):
%o A350538         for a in '2468':
%o A350538             for b in product('02468',repeat=l):
%o A350538                 k = int(a+''.join(b))
%o A350538                 if k > n and k % n == 0:
%o A350538                     return k # _Chai Wah Wu_, Jan 12 2022
%o A350538 (PARI) a(n) = my(k=2); while(#select(x->((x%2) == 1), digits(k*n)), k++); k*n; \\ _Michel Marcus_, Jan 12 2022
%Y A350538 Cf. A061807, A350536.
%Y A350538 Terms belong to A014263.
%K A350538 nonn,base
%O A350538 1,1
%A A350538 _Bernard Schott_, Jan 05 2022
%E A350538 More terms from _Michael S. Branicky_, Jan 05 2022