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A094676 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 and the second digit of m is not zero. +0
4
1, 210526315789473684, 3103448275862068965517241379, 410256, 510204081632653061224489795918367346938775, 6101694915254237288135593220338983050847457627118644067796, 7101449275362318840579, 8101265822784, 91011235955056179775280898876404494382022471 (list; graph; listen)
OFFSET

1,2

COMMENT

Here when the leftmost digit of m is shifted to the right end the number of digits may not decrease - compare A097717.

Least n-transposable number. A k-transposable number, 1<=k<=9, is one which is k times the number obtained when the left-most digit is moved to the end.

Rotating the most-significant digit in other bases defines related sequences: 1,2,9,4,35,558,2205,8,135,.. (base 2), 1,32,3,88,260,... (base 3), 1,18,279,4,68985,.. (base 4), 1,16,3348,411184,5,... (base 5) etc. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 30 2009]

REFERENCES

H. Camous, Jouer Avec Les Maths, "Chassez le naturel", Section I, Problem 3 pp. 20;31-2, Les Editions D'Organisation, Paris 1984.

L. A. Graham, Ingenious Mathematical Problems and Methods, "End At The Beginning", Problem 72 pp. 44;212-3 Dover NY 1959.

FORMULA

a(n) = n prepended to n*(10^m - n)/(10*n - 1), where m=A094224(n)-1.

EXAMPLE

a(4)=410256=4*102564

CROSSREFS

Sequence in context: A095433 A099727 A011530 this_sequence A054213 A080128 A132901

Adjacent sequences: A094673 A094674 A094675 this_sequence A094677 A094678 A094679

KEYWORD

fini,nonn,base,full

AUTHOR

Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 07 2004

EXTENSIONS

Edited by N. J. A. Sloane, Apr 13 2009

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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