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A352725 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of a(n) and a(n+1) have no common runs of consecutive 1's.

%I A352725 #13 Apr 01 2022 09:02:26
%S A352725 0,1,2,3,4,6,5,7,8,12,9,14,10,13,11,15,16,24,17,26,19,25,18,27,20,28,
%T A352725 21,30,22,29,23,31,32,48,33,50,35,49,34,51,36,54,37,55,38,52,39,53,40,
%U A352725 56,41,58,43,57,42,59,44,60,45,62,46,61,47,63,64,96,65,98
%N A352725 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of a(n) and a(n+1) have no common runs of consecutive 1's.
%C A352725 This sequence is a variant of A109812; here we consider runs of consecutive 1's, there individual 1's in binary expansions.
%C A352725 The binary expansions of two consecutive terms may share some 1's, but cannot have a common run of consecutive 1's (as given by A352724).
%H A352725 Rémy Sigrist, <a href="/A352725/b352725.txt">Table of n, a(n) for n = 0..8192</a>
%H A352725 Rémy Sigrist, <a href="/A352725/a352725.png">Scatterplot of the first 32769 terms</a>
%H A352725 Rémy Sigrist, <a href="/A352725/a352725.gp.txt">PARI program</a>
%e A352725 The first terms, alongside the corresponding partitions into runs of 1's, are:
%e A352725   n   a(n)  runs in a(n)
%e A352725   --  ----  ------------
%e A352725    0     0  []
%e A352725    1     1  [1]
%e A352725    2     2  [2]
%e A352725    3     3  [3]
%e A352725    4     4  [4]
%e A352725    5     6  [6]
%e A352725    6     5  [1, 4]
%e A352725    7     7  [7]
%e A352725    8     8  [8]
%e A352725    9    12  [12]
%e A352725   10     9  [1, 8]
%e A352725   11    14  [14]
%e A352725   12    10  [2, 8]
%e A352725   13    13  [1, 12]
%e A352725   14    11  [3, 8]
%e A352725   15    15  [15]
%e A352725   16    16  [16]
%o A352725 (PARI) See Links section.
%Y A352725 Cf. A109812, A332565, A352724.
%K A352725 nonn,base
%O A352725 0,3
%A A352725 _Rémy Sigrist_, Mar 30 2022