A158379 Period-lengths of the base-3 MR-expansions of the reciprocals of the positive integers.

2, 1, 2, 2, 4, 1, 6, 1, 2, 4, 4, 2, 2, 6, 4, 3, 16, 1, 18, 2, 6, 3, 8, 1, 20, 1, 2, 6, 28, 4, 30, 7, 4, 16, 10, 2, 18, 18, 2, 2, 8, 6, 42, 8, 4, 11, 18, 3, 42, 20, 16, 4, 52, 1, 20, 3, 18, 28, 26, 2, 10, 30, 6, 15, 10, 3, 22, 12, 8, 8, 28, 1, 12, 18, 20, 18, 28, 1, 78, 1, 2, 8, 38, 6, 14, 42, 28

Offset: 1

Author

John W. Layman, Mar 17 2009

Keywords

• nonn

Comments

See A136042 for the definition of the MR-expansion.

It appears that if p is a prime with 3 as a primitive root (A001122), then the MR-expansion of 1/p is periodic with period p-1.

The period lengths of the base-2 MR-expansions of the reciprocals of the positive integers are given in A136043.

Examples

			The base-3 MR-expansion of 1/5 is {2,1,0,1,2,1,0,1,...} because 1/5->3/5->9/5->4/5->12/5->7/5->2/5->6/5->1/5->..., indicating that MR(1/5,3) begins {2,1,0,1,...} and has period 4. Thus a(5)=4.
		

Crossrefs

Cf. A001122, A007733, A115591, A136042, A136043, A136044, A155072.