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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)
OFFSET
1,2
COMMENTS
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
LINKS
EXAMPLE
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).
MATHEMATICA
(*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}]
CROSSREFS
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 * A357515 A246111 A067818
KEYWORD
nonn,base
AUTHOR
Anton V. Chupin (chupin(X)icmm.ru), Apr 12, 2007
EXTENSIONS
Edited by N. J. A. Sloane, Apr 13 2009
Code and b-file corrected by Ray Chandler, Apr 29 2009
STATUS
approved

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Last modified March 19 07:19 EDT 2024. Contains 370954 sequences. (Running on oeis4.)