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COMMENT
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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]
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REFERENCES
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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.
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