A057508 Self-inverse permutation of natural numbers induced by the function 'reverse' (present in programming languages like Lisp, Scheme, Prolog and Haskell) when it acts on symbolless S-expressions encoded by A014486/A063171.

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 14, 11, 16, 19, 10, 15, 12, 17, 18, 13, 20, 21, 22, 23, 37, 28, 42, 51, 25, 39, 30, 44, 47, 33, 53, 56, 60, 24, 38, 29, 43, 52, 26, 40, 31, 45, 46, 32, 48, 49, 50, 27, 41, 34, 54, 55, 35, 57, 58, 59, 36, 61, 62, 63, 64, 65, 107, 79, 121, 149, 70

Offset

0,3

Links

Table of n, a(n) for n=0..70.

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

Index entries for the sequences induced by list functions of Lisp

Index entries for signature-permutations induced by Catalan automorphisms

Maple

Similar function for Maple lists can be implemented as: reverse := proc(a) if 0 = nops(a) then (a) else [op(reverse(cdr(a))), a[1]]; fi; end;

Prog

(Scheme) ;; Function implementing this automorphism on list-structures
(define (Rev1! s) (cond ((pair? s) (Rev1! (cdr s)) (Rol! s))) s) ;; Destructive variant, see A057509 for Rol!
(Scheme)
(define (Rev2! s) (cond ((pair? s) (Ror! s) (Rev2! (cdr s)))) s) ;; Another variant, see A057510 for Ror!

Crossrefs

The car/cdr-flipped conjugate of A069769, i.e. A057508(n) = A057163(A069769(A057163(n))). Cf. also A057164, A057509, A057510, A033538.

Sequence in context: A130945 A073285 A057512 * A057164 A085175 A130111

Adjacent sequences: A057505 A057506 A057507 * A057509 A057510 A057511

Keyword

nonn

Author

Antti Karttunen, Sep 03 2000

Status

approved