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Self-inverse permutation of nonnegative integers, "gray-blue" code: a(n) = A193231(A003188(n)).
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%I #10 Aug 30 2014 18:57:22

%S 0,1,2,3,6,7,4,5,10,11,8,9,12,13,14,15,30,31,28,29,24,25,26,27,20,21,

%T 22,23,18,19,16,17,34,35,32,33,36,37,38,39,40,41,42,43,46,47,44,45,60,

%U 61,62,63,58,59,56,57,54,55,52,53,48,49,50,51,102,103,100

%N Self-inverse permutation of nonnegative integers, "gray-blue" code: a(n) = A193231(A003188(n)).

%H Antti Karttunen, <a href="/A234613/b234613.txt">Table of n, a(n) for n = 0..8191</a>

%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, section 1.19 "Invertible transforms on words", pp. 49--55 [Cf. especially the identity 1.19-9d: gB = Bg^{-1} given on page 53].

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(n) = A193231(A003188(n)).

%F a(n) = A006068(A193231(n)).

%F a(n) = A193231(A234612(A193231(n))).

%o (Scheme)

%o (define (A234613 n) (A193231 (A003188 n)))

%o (define (A234613v2 n) (A006068 (A193231 n))) ;; Alternative two.

%Y Cf. A003188, A006068, A193231, A234612, A234024-A234027.

%K nonn

%O 0,3

%A _Antti Karttunen_, Dec 28 2013