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Search: id:A110732
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| A110732 |
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Let n = abc... where a,b,c ... are the digits. Then a(n) = least multiple of n of the form aaa...bbb...ccc..., with each digit having the same frequency f > 1; or 0 if no such number exists. |
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+0
2
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| 11, 22, 33, 44, 55, 66, 77, 88, 99, 1100, 1111, 0, 111111333333, 111111444444, 1155, 0, 11111111111111117777777777777777, 1188, 111111111111111111999999999999999999, 2200, 222222111111, 2222, 22222222222222222222223333333333333333333333, 0, 0
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OFFSET
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1,1
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COMMENT
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For odd n not a multiple of 5, a(n) is not 0, as every such odd number divides a (infinitely many) unary number of the type 11111...= (10^k-1)/9, by Fermat's little theorem. e.g. 13 divides 111111 hence a(13) = 111111333333. Zeros occur only for some powers/multiples of 2 and 5 as 25 does not divide 222555...etc. and 16 can not divide any number of the type 111...666...
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REFERENCES
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Amarnath Murthy, On the divisors of unary sequence, Smarandache Notions Journal, Vol-11, 2000.
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CROSSREFS
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Cf. A110733.
Sequence in context: A110745 A020338 A052191 this_sequence A044836 A033008 A082275
Adjacent sequences: A110729 A110730 A110731 this_sequence A110733 A110734 A110735
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KEYWORD
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base,easy,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 09 2005
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EXTENSIONS
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More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 06 2006
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