A071656 - OEIS

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

%S 0,1,3,2,7,6,8,4,5,17,16,18,14,15,20,19,22,9,10,21,11,12,13,45,44,46,

%T 42,43,48,47,50,37,38,49,39,40,41,54,53,55,51,52,61,60,63,23,24,62,25,

%U 26,27,57,56,64,28,29,58,30,31,32,59,33,34,35,36,129,128,130,126,127

%N Permutation of natural numbers induced by the automorphism car_cdr_robl! 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_robl! s) (cond ((not (pair? s))) ((not (pair? (cdr s))) (swap! s)) (else (car_cdr_robl! (car s)) (car_cdr_robl! (cdr s)) (robl! s))) s)

%o (define (robl! s) (let ((ex-car (car s))) (set-car! s (cddr s)) (set-cdr! (cdr s) ex-car) (swap! (cdr 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: A071655. The car/cdr-flipped conjugate of A071659, i.e. A071656(n) = A057163(A071659(A057163(n))). Cf. also A071657, A071658.

%K nonn

%O 0,3

%A _Antti Karttunen_, May 30 2002