

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.


15



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

1,2


REFERENCES

R. Sprague, Recreation in Mathematics, Problem 21 pp. 17; 478 Dover NY 1963.


LINKS



EXAMPLE

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.


MATHEMATICA

Min[Table[Block[{d=Ceiling[Log[10, n]], m=(10n1)/GCD[10n1, a]}, If[m!=1, While[PowerMod[10, d, m]!=n, d++ ], d=1]; ((10^(d+1)1) a n)/(10n1)], {a, 9}]] (* Anton V. Chupin (chupin(X)icmm.ru), Apr 12 2007 *)


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.


KEYWORD

nonn,base


AUTHOR



EXTENSIONS

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


STATUS

approved



