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A302844 Permutation of nonnegative integers: a(n) = A003188(A163356(n)).

%I A302844 #10 Apr 15 2018 15:06:46
%S A302844 0,1,2,3,12,15,14,13,10,9,8,11,4,5,6,7,24,27,26,25,30,31,28,29,18,19,
%T A302844 16,17,22,21,20,23,40,43,42,41,46,47,44,45,34,35,32,33,38,37,36,39,56,
%U A302844 57,58,59,52,55,54,53,50,49,48,51,60,61,62,63,192,195,194,193,198,199,196,197,202,203,200,201,206,205
%N A302844 Permutation of nonnegative integers: a(n) = A003188(A163356(n)).
%C A302844 When A207901, which is a multiplicative walk permutation, is composed from the right with this permutation, the result is A302781, another multiplicative walk permutation.
%H A302844 Antti Karttunen, <a href="/A302844/b302844.txt">Table of n, a(n) for n = 0..16383</a>
%H A302844 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A302844 a(n) = A003188(A163356(n)).
%F A302844 a(n) = A006068(A302846(n)).
%o A302844 (PARI)
%o A302844 A003188(n) = bitxor(n, n>>1);
%o A302844 A057300(n) = { my(t=1,s=0); while(n>0, if(1==(n%4),n++,if(2==(n%4),n--)); s += (n%4)*t; n >>= 2; t <<= 2); (s); };
%o A302844 A163356(n) = if(!n,n,my(i = (#binary(n)-1)\2, f = 4^i, d = (n\f)%4, r = (n%f)); (((((2+(i%2))^d)%5)-1)*f) + if(3==d,f-1-A163356(r),A057300(A163356(r)))); \\ _Antti Karttunen_, Apr 14 2018
%o A302844 A302844(n) = A003188(A163356(n));
%Y A302844 Cf. A302843 (inverse).
%Y A302844 Cf. A003188, A006068, A057300, A163356, A302846, A302781.
%K A302844 nonn
%O A302844 0,3
%A A302844 _Antti Karttunen_, Apr 14 2018