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.

1, 210526315789473684, 3103448275862068965517241379, 410256, 714285, 6101694915254237288135593220338983050847457627118644067796, 7101449275362318840579, 8101265822784, 91011235955056179775280898876404494382022471

Offset: 1

Author

Lekraj Beedassy, Jun 07 2004

Keywords

• nonn
• base
• fini
• full

Comments

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 leftmost digit is moved to the end.

Examples

			a(4) = 410256 = 4*102564.
		

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.

Crossrefs

Cf. A097717. A249596-A249599.

Formula

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

Extensions

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

a(5) corrected by Emilio Martín, Jul 28 2022