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Permutation of natural numbers induced by the automorphism cdr_robr_car! acting on the parenthesizations encoded by A014486.
7

%I #5 May 01 2014 02:47:41

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

%T 49,50,54,55,57,58,59,61,62,63,64,26,27,23,24,25,29,28,30,31,32,33,34,

%U 35,36,38,37,39,40,41,51,52,56,60,42,43,44,47,53,129,130,132,133,134

%N Permutation of natural numbers induced by the automorphism cdr_robr_car! 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 program 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 (cdr_robr_car! s) (cond ((not (pair? s))) ((not (pair? (car s))) (swap! s)) (else (cdr_robr_car! (cdr s)) (robr! s) (cdr_robr_car! (car 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: A072091 and also its car/cdr-flipped conjugate, i.e. A072090(n) = A057163(A072091(A057163(n))). Cf. also A071655-A071660, A072092-A072095.

%K nonn

%O 0,3

%A _Antti Karttunen_, Jun 25 2002