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.

1, 105263157894736842, 1034482758620689655172413793, 102564, 714285, 1016949152542372881355932203389830508474576271186440677966, 1014492753623188405797, 1012658227848, 10112359550561797752808988764044943820224719

Offset: 1

Author

Lekraj Beedassy, Sep 21 2004

Keywords

• nonn
• base

Examples

			We have a(5)=714285 since 714285/5=142857.
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.
		

References

• R. Sprague, Recreation in Mathematics, Problem 21 pp. 17; 47-8 Dover NY 1963.

Links

• A. V. Chupin, Table of n, a(n) for n=1..101
• A. V. Chupin, Table of n, a(n) for n=1..154

Crossrefs

A097717: when move L digit to R, divides by n (infinite)

A094676: when move L digit to R, divides by n, no. of digits is unchanged (finite)

A092697: when move R digit to L, multiplies by n (finite)

A128857 is the same sequence as A097717 except that m must begin with 1.

Not the same as A092697.

Cf. A249596 - A249599 (bases 2 to 5).

Programs

Mathematica

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 *)

Extensions

a(9) from Anton V. Chupin (chupin(X)icmm.ru), Apr 12 2007

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