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%I A300838 #13 Jul 22 2025 13:12:22
%S A300838 0,2,3,1,9,11,10,8,12,14,15,13,5,7,6,4,36,38,39,37,45,47,46,44,40,42,
%T A300838 43,41,33,35,34,32,48,50,51,49,57,59,58,56,60,62,63,61,53,55,54,52,20,
%U A300838 22,23,21,29,31,30,28,24,26,27,25,17,19,18,16,144,146,147,145,153,155,154,152,156,158,159,157,149,151
%N A300838 Permutation of nonnegative integers: a(n) = A057300(A003188(n)).
%C A300838 Like in binary Gray code A003188, also in this permutation the binary expansions of a(n) and a(n+1) differ always by just a single bit-position, that is, A000120(A003987(a(n),a(n+1))) = 1 for all n >= 0. Here A003987 computes bitwise-XOR of its two arguments. This is true for any composition P(A003188(n)), where P is a permutation that permutes the bit-positions of binary expansion of n in some way.
%C A300838 When composed with A052330 this gives a divisor-or-multiple permutation similar to A207901 and A302781.
%H A300838 Antti Karttunen, <a href="/A300838/b300838.txt">Table of n, a(n) for n = 0..16383</a>
%H A300838 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A300838 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A300838 a(n) = A057300(A003188(n)).
%o A300838 (PARI)
%o A300838 A003188(n) = bitxor(n, n>>1);
%o A300838 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 A300838 A300838(n) = A057300(A003188(n));
%Y A300838 Cf. A300839 (inverse permutation).
%Y A300838 Cf. also A003188, A163252, A302846 for other permutations satisfying the same condition.
%K A300838 nonn,base,easy
%O A300838 0,2
%A A300838 _Antti Karttunen_ and _Peter Munn_, Apr 15 2018