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%I #9 Jan 29 2014 15:04:37
%S 0,2,1,3,32,34,33,35,16,18,17,19,48,50,49,51,8,10,9,11,40,42,41,43,24,
%T 26,25,27,56,58,57,59,4,6,5,7,36,38,37,39,20,22,21,23,52,54,53,55,12,
%U 14,13,15,44,46,45,47,28,30,29,31,60,62,61,63,128,130,129,131,160,162
%N CGT-tree negating involution of nonnegative integers.
%C This involution negates game trees used in the combinatorial game theory, when they are encoded in the way explained in A106486.
%C Cycles are confined into ranges [a(n),a(n+1)[, where a(0)=0 and a(n+1)=2^(2*a(n)), i.e. the ranges are [0,0], [1,3], [4,255], [256,(2^512)-1], ...
%H Antti Karttunen, <a href="/A106485/b106485.txt">Table of n, a(n) for n = 0..1023</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o (Scheme:) (define (A106485 n) (let loop ((n n) (i 0) (s 0)) (cond ((zero? n) s) ((odd? n) (loop (/ (- n 1) 2) (1+ i) (+ s (if (even? i) (expt 2 (+ 1 (* 2 (A106485 (/ i 2))))) (expt 2 (* 2 (A106485 (/ (- i 1) 2)))))))) (else (loop (/ n 2) (1+ i) s)))))
%Y A057300 is a "shallow" version which just swaps the left and right options of the game tree, but does not reflect the subtrees themselves. Cf. A106486-A106487.
%K nonn
%O 0,2
%A _Antti Karttunen_, May 21 2005
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