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Smallest number m > 1 such that n * m = A350538(n) contains only even digits.
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%I #11 Jan 17 2022 11:21:49

%S 2,2,2,2,4,4,4,3,32,2,2,2,2,2,4,3,4,16,12,2,2,2,2,2,8,8,18,3,14,2,2,2,

%T 2,2,8,8,6,6,12,2,2,2,2,2,64,10,6,5,14,4,4,4,8,9,4,4,4,7,14,4,4,4,14,

%U 7,4,4,4,3,12,4,4,4,28,3,8,3,6,6,34,3,6,3,8,5,8

%N Smallest number m > 1 such that n * m = A350538(n) contains only even digits.

%C The smallest odd term is a(48) = 5 because 48*5 = 240.

%C Record values of a(n) are 2, 4, 32, 64, ...

%F a(n) = A350538(n) / n.

%e The smallest proper multiple of 9 with only even digits is A350538(9) = 288, as 288 = 9 * 32, a(9) = 32.

%t a[n_] := Module[{k = 2*n}, While[! AllTrue[IntegerDigits[k], EvenQ], k += n]; k/n]; Array[a, 100] (* _Amiram Eldar_, Jan 12 2022 *)

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

%Y Cf. A061807, A350536, A350537, A350538.

%K nonn,base

%O 1,1

%A _Bernard Schott_, Jan 12 2022

%E More terms from _Michel Marcus_, Jan 12 2022