A007886 Number of cycles induced by iterating the Gray-coding of an n-bit number: a(n+1) = a(n) + ( 2^n / C_n), where C_n = least power of 2 >= n (C_n is the length of the cycle).

1, 2, 3, 4, 6, 8, 12, 20, 36, 52, 84, 148, 276, 532, 1044, 2068, 4116, 6164, 10260, 18452, 34836, 67604, 133140, 264212, 526356, 1050644, 2099220, 4196372, 8390676, 16779284, 33556500, 67110932, 134219796, 201328660, 335546388, 603981844

Offset

0,2

Links

Table of n, a(n) for n=0..35.

J. Culberson, Mutation-Crossover Isomorphisms and the Construction of Discriminating Functions, Evolutionary Computation 2(3): 279-311, (1994).

J. A. Oteo and J. Ros, A Fractal Set from the Binary Reflected Gray Code, J. Phys. A: Math Gen. 38 (2005) 8935-8949.

Prog

(PARI) f(n) = 2^(n-1-log(n+.5)\log(2)) \\ A054243
a(n) = if (n<=1, n+1, a(n-1) + f(n-1));

Crossrefs

Cf. A054243.

Sequence in context: A156082 A018465 A127107 * A135108 A018515 A018253

Adjacent sequences: A007883 A007884 A007885 * A007887 A007888 A007889

Keyword

nonn

Author

Joe Culberson (joe(AT)cs.ualberta.ca)

Status

approved