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

1,3

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.

Links

Table of n, a(n) for n=1..82.

Example

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.

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 *)

Prog

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

Crossrefs

Indices of 0's give A296606.

Indices of 1's give A011531.

Sequence in context: A325972 A073441 A202325 * A199382 A254289 A373022

Adjacent sequences: A337081 A337082 A337083 * A337085 A337086 A337087

Keyword

nonn,base

Author

J. Lowell, Aug 14 2020

Status

approved