A072090 Permutation of natural numbers induced by the automorphism cdr_robr_car! acting on the parenthesizations encoded by A014486.

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, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 26, 27, 23, 24, 25, 29, 28, 30, 31, 32, 33, 34, 35, 36, 38, 37, 39, 40, 41, 51, 52, 56, 60, 42, 43, 44, 47, 53, 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 program 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 (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)
(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: A072091 and also its car/cdr-flipped conjugate, i.e. A072090(n) = A057163(A072091(A057163(n))). Cf. also A071655-A071660, A072092-A072095.

Sequence in context: A074680 A123496 A130370 * A130365 A130933 A130966

Adjacent sequences: A072087 A072088 A072089 * A072091 A072092 A072093

Keyword

nonn

Author

Antti Karttunen, Jun 25 2002

Status

approved