%I #6 Mar 31 2012 13:21:17
%S 0,1,2,3,5,4,6,7,10,11,8,9,12,13,14,15,21,20,22,23,16,17,18,19,24,25,
%T 26,27,28,29,30,31,42,43,40,41,44,45,46,47,32,33,34,35,36,37,38,39,48,
%U 49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,85,84,86,87,80,81,82,83
%N Permutation of nonnegative integers induced by Basilica group generating wreath recursion: a = (b,1), b = s(a,1), starting from the inactive (fixing) state a.
%H A. Karttunen, <a href="/A154443/b154443.txt">Table of n, a(n) for n = 0..2047</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o (MIT Scheme:) (define (A154443 n) (if (< n 2) n (let loop ((maskbit (A072376 n)) (p 0) (z n)) (cond ((zero? maskbit) z) ((not (zero? (modulo (floor->exact (/ n maskbit)) 2))) (- z (* p maskbit))) (else (loop (floor->exact (/ maskbit 2)) (- 1 p) (+ z (* p maskbit))))))))
%Y Inverse: A154444. a(n) = A154441(A153141(n)) = A054429(A154439(A054429(n))). Cf. A072376, A153141-A153142, A154435-A154436, A154439-A154448. Corresponds to A154453 in the group of Catalan bijections.
%K nonn,base
%O 0,3
%A _Antti Karttunen_, Jan 17 2009
%E Spelling/notation corrections by _Charles R Greathouse IV_, Mar 18 2010