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%I #14 Apr 25 2016 12:00:15
%S 1,2,3,4,5,12,7,8,19,10,11,6,51,56,15,16,71,76,9,20,21,44,23,48,13,
%T 204,25,112,455,240,31,32,271,568,143,38,307,18,79,40,83,42,43,22,179,
%U 184,47,24,783,26,27,102,819,50,207,14,1807,3640,911,120,3855
%N If the run lengths of the binary representation of n are [1+r_1, 1+r_2, 1+r_3, ..., 1+r_k], then those of a(n) are [1+(r_1), 1+(r_1 XOR r_2), 1+(r_1 XOR r_2 XOR r_3), ..., 1+(r_1 XOR ... XOR r_k)], where XOR denotes the XOR binary operator.
%C This is a permutation of the natural numbers with inverse permutation A225607.
%C The sequence (n, a(n), a(a(n)), a(a(a(n))),...) is periodic for any n.
%C The run lengths of the binary representation of a fixed point are of the form [1, 1,...,1, K] (any number of ones followed by any number).
%H Paul Tek, <a href="/A227987/b227987.txt">Table of n, a(n) for n = 1..10000</a>
%H Paul Tek, <a href="/A227987/a227987.txt">PERL program for this sequence</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e For n=927:
%e (1) binary representation of n = "1110011111",
%e (2) run lengths of n = [1+2,1+1,1+4],
%e (3) run lengths of a(n) = [1+(2),1+(2 XOR 1),1+(2 XOR 1 XOR 4)]=[3,4,8],
%e (4) binary representation of a(n) = "111000011111111",
%e (5) a(n) = 28927.
%o (Perl) See Links section.
%Y Cf. A056539, A226532, A225607 (inverse).
%K nonn,base
%O 1,2
%A _Paul Tek_, Aug 02 2013
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