A159863 a(3)(baseN) = least number m such that the quotient m/3 is obtained merely by shifting the leftmost digit (MSD) of m to the right end (LSD), and the multiple 3m by shifting the LSD of m to the MSD, in order of increasing number base, N.

10113, 101343, 1020412245351433, 1023, 10262054413, 103, 1034482758620689655172413793, 2076

Offset: 4

Author

William A. Hoffman III (whoff(AT)robill.com), Apr 24 2009

Keywords

• base
• nonn
• fini
• full

Comments

1001b2, 10b3 and 51b7 do not triple by specified shift and are not included although they allow MSD->LSD shift to make m/3. No 2-digit number qualifies because the shift is an exchange (e.g., 51b7/3=15b7). 2076b11 is the highest order number of this type to be represented without letter digits.

Examples

			2076b11/3=762b11 (2745/3=915) and 3*2076b11=6207b11 (3*2745=8235).
		

Links

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

Crossrefs

Cf. A023060, A159774.

See A160116 for these numbers written in base 10.

Extensions

Edited by Ray Chandler, May 02 2009