Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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