A078273 Smallest multiple of n other than n using only the digits of n (no limit on frequency).

11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 1111, 1212, 1131, 1414, 555, 1616, 1717, 1188, 1919, 200, 2121, 2222, 322, 2424, 225, 2262, 2727, 2828, 2929, 300, 1333, 3232, 3333, 3434, 3535, 3636, 333, 3838, 3393, 400, 4141, 4242, 344, 4444, 4455, 644, 4747, 4848

Offset

1,1

Comments

a(k) = 10k if k contains a zero. a(n) <= (10^d +1)*n where d is the number of digits in n. There are some patterns in which every digit is used exactly as many times as it occurs in n. (A008918 and A001232). (1) a(2178) = 8712, a(21978) = 87912, a(219978) = 879912, etc... with a(n)/n = 4. A derived pattern is a(21782178) = 87128712, a(217821782178) = 871287128712 etc. (2) a(1089) = 9801, a(10989) = 98901, a(109989)= 989901,... with a(n)/n = 9. More patterns can be derived on similar lines.

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

Example

a(30) = 300, a(2178) = 8712, a(1089) = 9801.

Mathematica

smn[n_]:=Module[{k=2}, While[!SubsetQ[IntegerDigits[n], IntegerDigits[ k*n]], k++]; k*n]; Array[smn, 50] (* Harvey P. Dale, Dec 03 2018 *)

Crossrefs

Cf. A008918, A001232.

Sequence in context: A302575 A302801 A067042 * A345391 A065571 A064544

Adjacent sequences: A078270 A078271 A078272 * A078274 A078275 A078276

Keyword

base,nonn

Author

Amarnath Murthy, Nov 24 2002

Extensions

Corrected and extended by Sean A. Irvine, Mar 09 2010

Status

approved