Search: id:A154447
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%I A154447
%S A154447 0,1,3,2,6,7,5,4,12,13,14,15,11,10,8,9,24,25,26,27,28,29,30,31,22,23,
%T A154447 21,20,16,17,18,19,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,44,
%U A154447 45,46,47,43,42,40,41,32,33,34,35,36,37,38,39,96,97,98,99,100,101,102
%N A154447 Permutation of non-negative integers induced by wreath recursion a=s(b,
               c), b=s(c,a), c=(c,c), starting from state b, rewriting bits from 
               the second most significant bit toward the least significant end.
%C A154447 This permutation of natural numbers is induced by the second generator 
               of group 2861 mentioned on page 144 of "Classification of groups 
               generated by 3-state automata over a 2-letter alphabet" paper. It 
               can be computed by starting scanning n's binary expansion rightward 
               from the second most significant bit, complementing every bit down 
               to and including A) either the first 0-bit at odd distance from the 
               most significant bit or B) the first 1-bit at even distance from 
               the most significant bit.
%H A154447 A. Karttunen, <a href="b154447.txt">Table of n, a(n) for n = 0..2047</
               a>
%H A154447 Bondarenko, Grigorchuk, Kravchenko, Muntyan, Nekrashevych, Savchuk, Sunic, 
               <a href="http://arxiv.org/abs/0803.3555">Classification of groups 
               generated by 3-state automata over a 2-letter alphabet</a>, p. 144.
%H A154447 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%e A154447 25 = 11001 in binary, the first zero-bit at odd distance from the msb 
               is at position 1 (distance 3) and the first one-bit at even distance 
               from the msb is at position 0 (distance 4), thus we stop at the former, 
               after complementing the bits 3-1, which gives us 10111 (23 in binary), 
               thus a(25)=23.
%o A154447 (MIT Scheme:) (define (A154447 n) (if (< n 2) n (let loop ((maskbit (A072376 
               n)) (p 0) (z n)) (cond ((zero? maskbit) z) ((= p (modulo (floor->
               exact (/ n maskbit)) 2)) (+ z (* (- 1 (* 2 p)) maskbit))) (else (loop 
               (floor->exact (/ maskbit 2)) (- 1 p) (- z (* (- 1 (* 2 p)) maskbit))))))))
%Y A154447 Inverse: A154448. a(n) = A054429(A154448(A054429(n))). Cf. A072376, A153141-A153142, 
               A154435-A154436, A154439-A154446. Corresponds to A154457 in the group 
               of Catalan bijections.
%Y A154447 Sequence in context: A120231 A083362 A153142 this_sequence A003188 A154435 
               A006042
%Y A154447 Adjacent sequences: A154444 A154445 A154446 this_sequence A154448 A154449 
               A154450
%K A154447 nonn,base
%O A154447 0,3
%A A154447 Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jan 17 2009

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