A337084 a(n) is the smallest nonzero digit d whose product d*n will contain the digit d, or 0 if no such digit exists.

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, 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, 5, 5, 1, 0, 5, 0, 5, 2, 3, 3, 3, 0, 1, 7

Offset: 1

Author

J. Lowell, Aug 14 2020

Keywords

• nonn
• base

Comments

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

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

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

Examples

			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.
		

Crossrefs

Indices of 0's give A296606.

Indices of 1's give A011531.

Programs

Mathematica

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 *)

PARI

a(n) = {for (d=1, 9, if (#select(x->(x==d), digits(n*d)), return (d));); return (0);} \\ Michel Marcus, Sep 13 2020