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

Author

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

Keywords

• nonn

Links

• 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.

Crossrefs

Cf. A054243.

Programs

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));