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A352726 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of n and a(n) have no common runs of consecutive 1's.

%I A352726 #17 Apr 01 2022 09:02:41
%S A352726 0,2,1,4,3,6,5,8,7,12,13,14,9,10,11,16,15,24,25,26,27,28,29,30,17,18,
%T A352726 19,20,21,22,23,32,31,48,49,50,51,54,52,53,55,56,57,58,59,60,61,62,33,
%U A352726 34,35,36,38,39,37,40,41,42,43,44,45,46,47,64,63,96,97,98
%N A352726 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of n and a(n) have no common runs of consecutive 1's.
%C A352726 This sequence is a self-inverse permutation of the nonnegative integers.
%C A352726 This sequence has similarities with A238757; here we consider runs of consecutive 1's, there individual 1's in binary expansions.
%C A352726 The binary expansion of n and a(n) may share some 1's, but cannot have a common run of consecutive 1's (as given by A352724).
%H A352726 Rémy Sigrist, <a href="/A352726/b352726.txt">Table of n, a(n) for n = 0..8192</a>
%H A352726 Rémy Sigrist, <a href="/A352726/a352726.png">Scatterplot of the first 32769 terms</a>
%H A352726 Rémy Sigrist, <a href="/A352726/a352726_2.png">Scatterplot of (x, y) such that x, y < 2^10 and the binary expansions of x and y have no common runs of consecutive 1's</a>
%H A352726 Rémy Sigrist, <a href="/A352726/a352726.gp.txt">PARI program</a>
%H A352726 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A352726 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A352726 The first terms, alongside the corresponding partitions into runs of 1's, are:
%e A352726   n   a(n)  runs in n  runs in a(n)
%e A352726   --  ----  ---------  ------------
%e A352726    0     0  []         []
%e A352726    1     2  [1]        [2]
%e A352726    2     1  [2]        [1]
%e A352726    3     4  [3]        [4]
%e A352726    4     3  [4]        [3]
%e A352726    5     6  [1, 4]     [6]
%e A352726    6     5  [6]        [1, 4]
%e A352726    7     8  [7]        [8]
%e A352726    8     7  [8]        [7]
%e A352726    9    12  [1, 8]     [12]
%e A352726   10    13  [2, 8]     [1, 12]
%e A352726   11    14  [3, 8]     [14]
%e A352726   12     9  [12]       [1, 8]
%e A352726   13    10  [1, 12]    [2, 8]
%e A352726   14    11  [14]       [3, 8]
%e A352726   15    16  [15]       [16]
%e A352726   16    15  [16]       [15]
%o A352726 (PARI) See Links section.
%Y A352726 Cf. A238757, A332022, A352724.
%K A352726 nonn,base
%O A352726 0,2
%A A352726 _Rémy Sigrist_, Mar 30 2022