A136044 -id:A136044 - cp's OEIS frontend

A136042 Base-2 MR-expansion of 1/29.

5, 4, 1, 2, 3, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 4, 1, 2, 3, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 4, 1, 2, 3, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 4, 1, 2, 3, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 4, 1, 2, 3, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 4, 1, 2, 3, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 4, 1, 2, 3, 1, 1, 1, 2, 1, 1, 3, 2, 1, 5, 4, 1, 2, 3, 1, 1

Offset: 1

John W. Layman, Dec 12 2007

The base-m MR-expansion of a positive real number x, denoted by MR(x,m), is the integer sequence {s(1),s(2),s(3),...}, where s(i) is the smallest exponent d such that (m^d)x(i)>1 and where x(i+1)=(m^d)x(i)-1, with the initialization x(1)=x. The base-2 MR-expansion of 1/29 is periodic with period length 14. Further computational results (see A136043) suggest that if p is a prime with 2 as a primitive root, then the base-2 MR-expansion of 1/p is periodic with period (p-1)/2. This has been confirmed for primes up to 2000. The base-2 MR-expansion of e=2.71828... is given in A136044.

			The MR-expansion of 1/5 using m=2 is {3,1,3,1,3,1,3,1,...}, because 1/5->2/5->4/5->8/5->3/5->6/5->1/5->... indicating that MR(1/5,2) begins {3,1,...} and has period length 2.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A136043, A136044, A158379.

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

Original entry on oeis.org

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

John W. Layman, Mar 17 2009

nonn

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.

			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.

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

cp's OEIS Frontend

A136042 Base-2 MR-expansion of 1/29.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs