A071659 Permutation of natural numbers induced by the automorphism car_cdr_robr! acting on the parenthesizations encoded by A014486.

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, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 26, 27, 23, 25, 24, 38, 37, 42, 44, 47, 51, 53, 56, 60, 29, 28, 30, 32, 31, 39, 40, 43, 52, 33, 34, 35, 41, 36, 129, 130, 132, 133, 134

Offset

0,3

Links

Table of n, a(n) for n=0..69.

A. Karttunen, Gatomorphisms (Includes the complete Scheme source for computing this sequence)

Index entries for sequences that are permutations of the natural numbers

Prog

(Scheme function implementing this automorphism on list-structures:)
(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)
(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))
(define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))

Crossrefs

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

Sequence in context: A069774 A089861 A072092 * A130931 A130962 A130367

Adjacent sequences: A071656 A071657 A071658 * A071660 A071661 A071662

Keyword

nonn

Author

Antti Karttunen, May 30 2002

Status

approved