A380997 a(n) is the least number with exactly 2 different decimal digits that is a multiple of n.

10, 10, 12, 12, 10, 12, 14, 16, 18, 10, 110, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 110, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 330, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 220, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 110, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 330, 67, 68, 69, 70, 71, 72, 73

Offset: 1

Author

Robert Israel, Feb 11 2025

Keywords

• nonn
• base
• look

Comments

a(n) is the least multiple of n that is in A031955.

Examples

			a(22) = 110 because 110 has two different decimal digits 0 and 1, is a multiple of 22, and no smaller multiple of 22 works.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A031955.

Programs

Maple

f:= proc(n) local d,i,s,S;
       S:= select(t -> nops(convert(convert(t*n mod 100,base,10),set)) <= 2, [$1..99] );
       for d from 3 do
         S:= select(s -> nops(convert(convert(s*n mod 10^d,base,10),set)) <= 2,
               [seq(seq(s+i*10^(d-1),s = S),i=0..9)]);
         for s in S do if nops(convert(convert(s*n,base,10),set)) = 2  then return s*n fi od;
       od;
end proc:
map(f, [$1..1000]);

Mathematica

a[n_]:=Module[{k=n}, While[Length[DeleteDuplicates[IntegerDigits[k]]]!=2, k+=n]; k]; Array[a,73] (* Stefano Spezia, Feb 13 2025 *)

PARI

a(n) = my(k=n); while(#Set(digits(k)) != 2, k+=n); k; \\ Michel Marcus, Feb 13 2025