cp's OEIS Frontend

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).

%I A007886 #14 Mar 07 2024 07:26:32
%S A007886 1,2,3,4,6,8,12,20,36,52,84,148,276,532,1044,2068,4116,6164,10260,
%T A007886 18452,34836,67604,133140,264212,526356,1050644,2099220,4196372,
%U A007886 8390676,16779284,33556500,67110932,134219796,201328660,335546388,603981844
%N 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).
%H A007886 J. Culberson, <a href="https://doi.org/10.1162/evco.1994.2.3.279">Mutation-Crossover Isomorphisms and the Construction of Discriminating Functions</a>, Evolutionary Computation 2(3): 279-311, (1994).
%H A007886 J. A. Oteo and J. Ros, <a href="https://doi.org/10.1088/0305-4470/38/41/007">A Fractal Set from the Binary Reflected Gray Code</a>, J. Phys. A: Math Gen. 38 (2005) 8935-8949.
%o A007886 (PARI) f(n) = 2^(n-1-log(n+.5)\log(2)) \\ A054243
%o A007886 a(n) = if (n<=1, n+1, a(n-1) + f(n-1));
%Y A007886 Cf. A054243.
%K A007886 nonn
%O A007886 0,2
%A A007886 Joe Culberson (joe(AT)cs.ualberta.ca)