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%I #13 Apr 01 2022 09:02:26
%S 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 21,30,22,29,23,31,32,48,33,50,35,49,34,51,36,54,37,55,38,52,39,53,40,
%U 56,41,58,43,57,42,59,44,60,45,62,46,61,47,63,64,96,65,98
%N 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 This sequence is a variant of A109812; here we consider runs of consecutive 1's, there individual 1's in binary expansions.
%C 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 Rémy Sigrist, <a href="/A352725/b352725.txt">Table of n, a(n) for n = 0..8192</a>
%H Rémy Sigrist, <a href="/A352725/a352725.png">Scatterplot of the first 32769 terms</a>
%H Rémy Sigrist, <a href="/A352725/a352725.gp.txt">PARI program</a>
%e The first terms, alongside the corresponding partitions into runs of 1's, are:
%e n a(n) runs in a(n)
%e -- ---- ------------
%e 0 0 []
%e 1 1 [1]
%e 2 2 [2]
%e 3 3 [3]
%e 4 4 [4]
%e 5 6 [6]
%e 6 5 [1, 4]
%e 7 7 [7]
%e 8 8 [8]
%e 9 12 [12]
%e 10 9 [1, 8]
%e 11 14 [14]
%e 12 10 [2, 8]
%e 13 13 [1, 12]
%e 14 11 [3, 8]
%e 15 15 [15]
%e 16 16 [16]
%o (PARI) See Links section.
%Y Cf. A109812, A332565, A352724.
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Mar 30 2022
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