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Search: id:A097717
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| A097717 |
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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. |
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5
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| 1, 105263157894736842, 1034482758620689655172413793, 102564, 714285, 1016949152542372881355932203389830508474576271186440677966, 1014492753623188405797, 1012658227848, 10112359550561797752808988764044943820224719
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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R. Sprague, Recreation in Mathematics, Problem 21 pp. 17; 47-8 Dover NY 1963.
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LINKS
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A. V. Chupin, Table of n, a(n) for n=1..101
A. V. Chupin, Table of n, a(n) for n=1..154
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EXAMPLE
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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.
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MATHEMATICA
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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
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CROSSREFS
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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.
Sequence in context: A008923 A146088 A092697 this_sequence A128857 A067818 A095433
Adjacent sequences: A097714 A097715 A097716 this_sequence A097718 A097719 A097720
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KEYWORD
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nonn,base
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Sep 21 2004
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EXTENSIONS
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a(9) from Anton V. Chupin (chupin(X)icmm.ru), Apr 12, 2007
Code and b-file corrected by Ray Chandler (rayjchandler(AT)sbcglobal.net), Apr 29 2009
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