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A078273
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Smallest multiple of n other than n using only the digits of n (no limit on frequency).
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0
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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
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1,1
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..48.
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EXAMPLE
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a(3) = 300, a(2178)=8712, a(1089) = 9801.,
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CROSSREFS
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Cf. A008918, A001232.
Sequence in context: A044851 A160861 A067042 * A065571 A064544 A083967
Adjacent sequences: A078270 A078271 A078272 * A078274 A078275 A078276
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 24 2002
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EXTENSIONS
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Corrected and extended by Sean A. Irvine, Mar 09 2010
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STATUS
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approved
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