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^A128858(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
A. V. Chupin, Table of n, a(n) for n=1..101
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}]
PROG
(Python)
from sympy import n_order
def A128857(n): return n*(10**n_order(10, (m:=10*n-1))-1)//m # Chai Wah Wu, Apr 09 2024
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
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