A094224 -id:A094224 - cp's OEIS frontend

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

Lekraj Beedassy, Jun 07 2004

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.

			a(4) = 410256 = 4*102564.

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.

Cf. A097717. A249596-A249599.

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

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

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

A159774 Least number m, written in base n, such that m/2 is obtained merely by shifting the leftmost digit of m to the right end, and 2m by shifting the rightmost digit of m to the left end, digits defined in base n.

Original entry on oeis.org

1012, 102, 102342, 1031345242, 103524563142, 1042, 10467842, 105263157894736842, 316, 10631694842

Offset: 3

William A. Hoffman III (whoff(AT)robill.com), Apr 21 2009

10(b2) and 31(b5) do not both halve and double by rotations. No 2-digit answer can meet the description, so the sequence begins with a base 3 value.

			1042(b8)/2 = 421(b8) and 1042(b8)*2 = 2104(b8)
316 (base 11) = 380 (base 10), 163 (base 11) = 190 (base 10), 631 (base 11) = 760 (base 10).

W. A. Hoffman III, Algorithm to compute terms.

Cf. A092697, A097717, A094224, A094676, A158877.

See A147514 for these numbers written in base 10.

Offset corrected by N. J. A. Sloane, Apr 23 2009
a(11) corrected. To indicate that terms from base n=13 on need digits larger than 9, keywords fini, full added. - Ray Chandler and R. J. Mathar, Apr 23 2009
Edited by Ray Chandler, May 02 2009

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Examples

References

Crossrefs

Formula

Extensions