

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

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


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.
Not the same as A092697.
Cf. A249596  A249599 (bases 2 to 5).
Sequence in context: A146088 A217592 A092697 * A128857 A246111 A067818
Adjacent sequences: A097714 A097715 A097716 * A097718 A097719 A097720


KEYWORD

nonn,base


AUTHOR

Lekraj Beedassy, Sep 21 2004


EXTENSIONS

a(9) from Anton V. Chupin (chupin(X)icmm.ru), Apr 12 2007
Code and bfile corrected by Ray Chandler, Apr 29 2009


STATUS

approved



