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

1,1

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.

Links

Table of n, a(n) for n=1..87.

Example

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.

Sequence in context: A244329 A003165 A337679 * A122838 A070306 A355639

Adjacent sequences: A158376 A158377 A158378 * A158380 A158381 A158382

Keyword

nonn

Author

John W. Layman, Mar 17 2009

Status

approved