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

Author

John W. Layman, Dec 12 2007

Keywords

• nonn
• easy

Comments

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A136043, A136044, A158379.