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.

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

Offset: 3

Author

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

Keywords

• base
• nonn
• fini
• full

Comments

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.

Examples

			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).
		

Links

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

Crossrefs

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

See A147514 for these numbers written in base 10.

Extensions

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