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

Author

Amarnath Murthy, Nov 24 2002

Keywords

• base
• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A008918, A001232.

Programs

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 *)

Extensions

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