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A154437 Permutation of nonnegative integers: A059893-conjugate of A154435.

%I A154437 #13 Apr 09 2020 22:22:31
%S A154437 0,1,3,2,5,6,7,4,13,10,11,12,9,14,15,8,21,26,27,20,25,22,23,24,29,18,
%T A154437 19,28,17,30,31,16,53,42,43,52,41,54,55,40,45,50,51,44,49,46,47,48,37,
%U A154437 58,59,36,57,38,39,56,61,34,35,60,33,62,63,32,85,106,107,84,105,86,87
%N A154437 Permutation of nonnegative integers: A059893-conjugate of A154435.
%C A154437 This permutation is induced by the same Lamplighter group generating wreath recursion (binary transducer) as A154435, starting from the active (swapping) state a, but in contrast to it, this one rewrites the bits from the least significant end up to the second most significant bit.
%H A154437 A. Karttunen, <a href="/A154437/b154437.txt">Table of n, a(n) for n = 0..2047</a>
%H A154437 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A154437 From _Yosu Yurramendi_, Feb 23 2020: (Start)
%F A154437 a(n) = A054429(A284459(n)) = A258996(A153154(n)) = A284459(A065190(n)).
%F A154437 a(1) = 1; for n > 0, a(2*n) = 2*a(A065190(n)) + 1, a(2*n+1) = 2*a(n). (End)
%o A154437 (R)
%o A154437 maxn <- 63 # by choice
%o A154437 a <- c(1,3,2)
%o A154437 for(n in 2:maxn){
%o A154437 a[2*n+1] <- 2*a[n]
%o A154437 if(n%%2 == 0) a[2*n] <- 2*a[n+1] + 1
%o A154437 else          a[2*n] <- 2*a[n-1] + 1
%o A154437 }
%o A154437 (a <- c(0,a))
%o A154437 # _Yosu Yurramendi_, Feb 23 2020
%Y A154437 Inverse: A154438. a(n) = A059893(A154435(A059893(n))) = A054429(A153154(A054429(n))).
%K A154437 nonn,base
%O A154437 0,3
%A A154437 _Antti Karttunen_, Jan 17 2009