

A078273


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


1



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
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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 * A065571 A064544 A083967
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



