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 A072094 Permutation of natural numbers induced by the automorphism cdr_robr_cdr! acting on the parenthesizations encoded by A014486. 4

%I

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

%T 49,50,54,55,57,58,59,61,62,63,64,35,36,32,31,34,26,27,24,23,25,29,28,

%U 30,33,41,40,38,37,39,43,42,44,47,52,51,53,56,60,129,130,132,133,134

%N Permutation of natural numbers induced by the automorphism cdr_robr_cdr! 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_cdr! s) (cond ((not (pair? s))) ((not (pair? (car s))) (swap! s)) (else (cdr_robr_cdr! (cdr s)) (robr! s) (cdr_robr_cdr! (cdr 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: A072095. The car/cdr-flipped conjugate of A072093, i.e. A072094(n) = A057163(A072093(A057163(n))). Cf. also A071655-A071660, A072090-A072091.

%K nonn

%O 0,3

%A _Antti Karttunen_, Jun 25 2002

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