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A302845 Permutation of nonnegative integers: a(n) = A163355(A064707(n)).

%I A302845 #8 Apr 15 2018 15:06:52
%S A302845 0,1,3,2,15,14,12,13,5,6,4,7,10,9,11,8,21,20,22,23,16,19,17,18,26,27,
%T A302845 25,24,31,28,30,29,63,62,60,61,48,49,51,50,58,57,59,56,53,54,52,55,42,
%U A302845 43,41,40,47,44,46,45,37,36,38,39,32,35,33,34,255,254,252,253,240,241,243,242,250,249,251,248,245,246,244
%N A302845 Permutation of nonnegative integers: a(n) = A163355(A064707(n)).
%H A302845 Antti Karttunen, <a href="/A302845/b302845.txt">Table of n, a(n) for n = 0..16383</a>
%H A302845 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A302845 a(n) = A163355(A064707(n)).
%F A302845 a(n) = A302843(A006068(n)).
%o A302845 (PARI)
%o A302845 A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ From A006068
%o A302845 A064707(n) = A006068(A006068(n));
%o A302845 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 A302845 A163355(n) = if(!n,n,my(i = (#binary(n)-1)\2, f = 4^i, d = (n\f)%4, r = (n%f)); if(((1==d)&&!(i%2))||((2==d)&&(i%2)), f+A163355(A057300(r)), if(3==d,f+f+A163355(A057300(r)), (3*f)+A163355(f-1-r))));
%o A302845 A302845(n) = A163355(A064707(n));
%Y A302845 Cf. A302846 (inverse).
%Y A302845 Cf. A006068, A057300, A064707, A163355, A302843, A302782.
%K A302845 nonn
%O A302845 0,3
%A A302845 _Antti Karttunen_, Apr 14 2018