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Permutation of natural numbers induced by the automorphism car_cdr_robr! acting on the parenthesizations encoded by A014486.
6

%I #5 Apr 30 2014 01:53:47

%S 0,1,3,2,7,8,4,6,5,17,18,20,21,22,10,9,14,16,19,11,12,15,13,45,46,48,

%T 49,50,54,55,57,58,59,61,62,63,64,26,27,23,25,24,38,37,42,44,47,51,53,

%U 56,60,29,28,30,32,31,39,40,43,52,33,34,35,41,36,129,130,132,133,134

%N Permutation of natural numbers induced by the automorphism car_cdr_robr! acting on the parenthesizations encoded by A014486.

%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> (Includes the complete Scheme source for computing this sequence)

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

%o (Scheme function implementing this automorphism on list-structures:)

%o (define (car_cdr_robr! s) (cond ((not (pair? s))) ((not (pair? (car s))) (swap! s)) (else (car_cdr_robr! (car s)) (car_cdr_robr! (cdr s)) (robr! s))) s)

%o (define (robr! s) (let ((ex-cdr (cdr s))) (set-cdr! s (caar s)) (set-car! (car s) ex-cdr) (swap! (car s)) (swap! s) s))

%o (define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))

%Y Inverse permutation: A071660. The car/cdr-flipped conjugate of A071656, i.e. A071659(n) = A057163(A071656(A057163(n))). Cf. also A071657, A071658.

%K nonn

%O 0,3

%A _Antti Karttunen_, May 30 2002