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A097717 a(n) = least number m such that the quotient m/n is obtained merely by shifting the leftmost digit of m to the right end.

%I A097717 #18 Dec 19 2016 05:42:23
%S A097717 1,105263157894736842,1034482758620689655172413793,102564,714285,
%T A097717 1016949152542372881355932203389830508474576271186440677966,
%U A097717 1014492753623188405797,1012658227848,10112359550561797752808988764044943820224719
%N A097717 a(n) = least number m such that the quotient m/n is obtained merely by shifting the leftmost digit of m to the right end.
%D A097717 R. Sprague, Recreation in Mathematics, Problem 21 pp. 17; 47-8 Dover NY 1963.
%H A097717 A. V. Chupin, <a href="/A097717/b097717.txt">Table of n, a(n) for n=1..101</a>
%H A097717 A. V. Chupin, <a href="/A097717/a097717.txt">Table of n, a(n) for n=1..154</a>
%e A097717 We have a(5)=714285 since 714285/5=142857.
%e A097717 Likewise, a(4)=102564 since this is the smallest number followed by 205128, 307692, 410256, 512820, 615384, 717948, 820512, 923076, ... which all get divided by 4 when the first digit is made last.
%t A097717 Min[Table[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)], {a,9}]] (* Anton V. Chupin (chupin(X)icmm.ru), Apr 12 2007 *)
%Y A097717 A097717: when move L digit to R, divides by n (infinite)
%Y A097717 A094676: when move L digit to R, divides by n, no. of digits is unchanged (finite)
%Y A097717 A092697: when move R digit to L, multiplies by n (finite)
%Y A097717 A128857 is the same sequence as A097717 except that m must begin with 1.
%Y A097717 Not the same as A092697.
%Y A097717 Cf. A249596 - A249599 (bases 2 to 5).
%K A097717 nonn,base
%O A097717 1,2
%A A097717 _Lekraj Beedassy_, Sep 21 2004
%E A097717 a(9) from Anton V. Chupin (chupin(X)icmm.ru), Apr 12 2007
%E A097717 Code and b-file corrected by _Ray Chandler_, Apr 29 2009