login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

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=(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 *)

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 b-file corrected by Ray Chandler, Apr 29 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)