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A128857 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. 4
1, 105263157894736842, 1034482758620689655172413793, 102564, 102040816326530612244897959183673469387755, 1016949152542372881355932203389830508474576271186440677966 (list; graph; refs; listen; history; text; internal format)



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


A. V. Chupin, Table of n, a(n) for n=1..101

G. P. Michon, Integers that are divided by k if their digits are rotated left.


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).


(*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}]


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

Sequence in context: A217592 A092697 A097717 * A246111 A067818 A262560

Adjacent sequences:  A128854 A128855 A128856 * A128858 A128859 A128860




Anton V. Chupin (chupin(X)icmm.ru), Apr 12, 2007


Edited by N. J. A. Sloane, Apr 13 2009

Code and b-file corrected by Ray Chandler, Apr 29 2009



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Last modified September 19 18:32 EDT 2017. Contains 292244 sequences.