A136043 Period-lengths of the base-2 MR-expansions of the reciprocals of the positive integers.

1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 5, 1, 6, 1, 1, 1, 4, 3, 9, 2, 2, 5, 4, 1, 10, 6, 9, 1, 14, 1, 1, 1, 5, 4, 5, 3, 18, 9, 4, 2, 10, 2, 7, 5, 5, 4, 9, 1, 10, 10, 2, 6, 26, 9, 8, 1, 9, 14, 29, 1, 30, 1, 1, 1, 6, 5, 33, 4, 11, 5, 14, 3, 3, 18, 9, 9, 15, 4, 17, 2, 27, 10, 41, 2, 2, 7, 11, 5, 4, 5, 4, 4, 3, 9, 14

Offset: 1

Author

John W. Layman, Dec 12 2007

Keywords

• nonn

Comments

It appears that if p is a prime with 2 as a primitive root (A001122), then a(p)=(p-1)/2. This has been confirmed for primes up to 2000. See A136042 for the definition of the MR-expansion of a positive real number.

Examples

			In A136042 it is shown that the base-2 MR-expansion of 1/5 is {3,1,3,1,3,1,3,1,...}, with period-length 2, so a(5)=2.
		

Crossrefs

Cf. A001122, A136042, A135044, A119513, A038553.

Formula

a(n) = 1 if n is a power of 2. It seems that otherwise a(n) = A119513(n). - Andrei Zabolotskii, Jul 28 2025