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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A031955.

Sequence in context: A215511 A280105 A173198 * A377565 A111381 A369604

Adjacent sequences: A380994 A380995 A380996 * A380998 A380999 A381000

Keyword

nonn,base,look

Author

Robert Israel, Feb 11 2025

Status

approved