A337084 - OEIS

%I #31 Sep 21 2020 12:12:05

%S 1,0,5,0,5,2,5,0,5,1,1,1,1,1,1,1,1,1,1,0,1,9,5,0,5,2,5,6,5,5,1,0,5,0,

%T 4,2,4,0,5,0,1,0,5,3,3,2,5,8,5,5,1,0,5,7,5,2,5,0,5,2,1,2,2,2,5,2,5,7,

%U 5,5,1,0,5,0,5,2,3,3,3,0,1,7

%N a(n) is the smallest nonzero digit d whose product d*n will contain the digit d, or 0 if no such digit exists.

%C a(n) = 1 for all numbers that contain the digit 1.

%C For all numbers with 6 followed by a digit in the 0-4 interval, a(n) is 1 or 2.

%C For all numbers with an odd digit followed by a 0, a(n) is in the 1-5 interval.

%e a(22) = 9 because none of 22*1 to 22*8 contain the digit that we multiplied 22 by to get the product, but 22*9 = 198 which contains the digit 9.

%t a[n_] := Module[{d = 1}, While[d < 10 && ! MemberQ[IntegerDigits[n*d], d], d++]; If[d < 10, d, 0]]; Array[a, 100] (* _Amiram Eldar_, Aug 15 2020 *)

%o (PARI) a(n) = {for (d=1, 9, if (#select(x->(x==d), digits(n*d)), return (d));); return (0);} \\ _Michel Marcus_, Sep 13 2020

%Y Indices of 0's give A296606.

%Y Indices of 1's give A011531.

%K nonn,base

%O 1,3

%A _J. Lowell_, Aug 14 2020