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A128857
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a(n) = least number m beginning with 1 such that the quotient m/n is obtained merely by shifting the leftmost digit 1 of m to the right end.
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4
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OFFSET
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1,2
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COMMENTS
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a(n) is simply the decimal period of the fraction n/(10n-1). Thus, we have: n/(10n-1) = a(n)/(10^A128857(n)-1). With the usual convention that the decimal period of 0 is zero, that definition would allow the extension a(0)=0. a(n) is also the period of the decadic integer -n/(10n-1). - Gerard P. Michon, Oct 31 2012
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LINKS
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EXAMPLE
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a(4) = 102564 since this is the smallest number that begins with 1 and which is divided by 4 when the first digit 1 is made the last digit (102564/4 = 25641).
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MATHEMATICA
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(*Moving digits a:*) Give[a_, n_]:=Block[{d=Ceiling[Log[10, n]], m=(10n-1)/GCD[10n-1, a]}, If[m!=1, While[PowerMod[10, d, m]!=n, d++ ], d=1]; ((10^(d+1)-1) a n)/(10n-1)]; Table[Give[1, n], {n, 101}]
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CROSSREFS
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Minimal numbers for shifting any digit from the left to the right (not only 1) are in A097717.
By accident, the nine terms of A092697 coincide with the first nine terms of the present sequence. - N. J. A. Sloane, Apr 13 2009
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KEYWORD
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nonn,base
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AUTHOR
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Anton V. Chupin (chupin(X)icmm.ru), Apr 12, 2007
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EXTENSIONS
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STATUS
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approved
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