A078249 Smallest multiple of n using all the digits other than used by n, or 0 if no such number exists.

203456789, 103456798, 102456789, 102357896, 123467890, 102345798, 102345698, 102345976, 102345678, 0, 203548697, 30457896, 20465978, 20356798, 23467890, 20357984, 20358469, 20345796, 20346587, 0, 30457896, 103465978, 10456789

Offset

1,1

Comments

a(n) = 0 if n==0 (mod 10), n ends in 5 and uses 0, n uses all even digits, or n uses all 9 nonzero digits.

Links

Table of n, a(n) for n=1..23.

Mathematica

sp[n_]:=Module[{digs=Complement[Range[0, 9], IntegerDigits[n]]}, Min[ Select[ FromDigits/@ Permutations[digs], IntegerLength[#]==(10-Length[ Union[ IntegerDigits[n]]])&&Divisible[#, n]&]]]; Array[sp, 25]/.\[Infinity]->0 (* Harvey P. Dale, Aug 17 2021 *)

Crossrefs

Sequence in context: A132205 A358019 A015427 * A243363 A273094 A226079

Adjacent sequences: A078246 A078247 A078248 * A078250 A078251 A078252

Keyword

base,nonn

Author

Amarnath Murthy, Nov 23 2002

Extensions

More terms from Hans Havermann, Jan 19 2004

Status

approved