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A352728 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of n and a(n) have exactly one common run of consecutive 1's.

%I A352728 #14 Apr 01 2022 09:03:17
%S A352728 1,2,3,4,9,6,7,8,5,11,10,12,17,14,15,16,13,19,18,22,23,20,21,24,26,25,
%T A352728 35,28,33,30,31,32,29,36,27,34,38,37,40,39,44,45,46,41,42,43,79,48,50,
%U A352728 49,52,51,54,53,71,56,58,57,67,60,65,62,63,64,61,68,59
%N A352728 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of n and a(n) have exactly one common run of consecutive 1's.
%C A352728 This sequence is a self-inverse permutation of the nonnegative integers.
%C A352728 This sequence is a variant of A238758; here we consider runs of consecutive 1's, there individual 1's in binary expansions.
%C A352728 We only consider runs of consecutive 1's that completely match in binary expansions of n and a(n), not simply single common 1's.
%H A352728 Rémy Sigrist, <a href="/A352728/b352728.txt">Table of n, a(n) for n = 1..8192</a>
%H A352728 Rémy Sigrist, <a href="/A352728/a352728.png">Scatterplot of the first 24574 terms</a>
%H A352728 Rémy Sigrist, <a href="/A352728/a352728_1.png">Scatterplot of (x, y) such that x, y < 2^10 and the binary expansions of x and y exactly one common run of consecutive 1's</a>
%H A352728 Rémy Sigrist, <a href="/A352728/a352728.gp.txt">PARI program</a>
%H A352728 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A352728 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A352728 The first terms, alongside the corresponding runs of 1's in binary expansions, are:
%e A352728   n   a(n)  runs in n  runs in a(n)
%e A352728   --  ----  ---------  ------------
%e A352728    1     1  [1]        [1]
%e A352728    2     2  [2]        [2]
%e A352728    3     3  [3]        [3]
%e A352728    4     4  [4]        [4]
%e A352728    5     9  [1, 4]     [1, 8]
%e A352728    6     6  [6]        [6]
%e A352728    7     7  [7]        [7]
%e A352728    8     8  [8]        [8]
%e A352728    9     5  [1, 8]     [1, 4]
%e A352728   10    11  [2, 8]     [3, 8]
%e A352728   11    10  [3, 8]     [2, 8]
%e A352728   12    12  [12]       [12]
%e A352728   13    17  [1, 12]    [1, 16]
%e A352728   14    14  [14]       [14]
%e A352728   15    15  [15]       [15]
%e A352728   16    16  [16]       [16]
%o A352728 (PARI) See Links section.
%Y A352728 Cf. A238758, A352726.
%K A352728 nonn,base
%O A352728 1,2
%A A352728 _Rémy Sigrist_, Mar 30 2022