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Binary sequence of itself (minus signs are delimiters, see the Comments section for explanations).
1

%I #20 Oct 17 2020 02:19:44

%S 0,-1,-3,1,-5,-7,2,3,-9,5,7,-11,4,-13,9,-15,6,8,11,-17,10,13,-19,15,

%T 17,-21,-23,-25,12,14,-27,-29,19,-31,16,18,21,-33,-35,20,23,-37,25,22,

%U -39,24,26,28,-41,-43,-45,-47,27,29,-49,-2,-51,-53,31,-55,-57,30,32,33,-59,-61,34,35,-63,-65,37,39,-67,36,-69,-71,38,-73,41,-75,40

%N Binary sequence of itself (minus signs are delimiters, see the Comments section for explanations).

%C Replace all even terms by a 0, odd terms by a 1. Consider now the minus signs as chunks' delimiters of concatenated 1's and 0's. The successive chunks are the binary equivalents of the sequence's term. This is the lexicographically earliest sequence having this property.

%H Jean-Marc Falcoz, <a href="/A336301/b336301.txt">Table of n, a(n) for n = 1..50000</a>

%e The sequence starts (plus signs added for readability):

%e 0,-1,-3,+1,-5,-7,+2,+3,-9,+5,+7,-11,+4,-k,...

%e We replace every even term by 0, every odd term by 1:

%e 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, ...

%e The former minus signs now delimit the binary chunks:

%e 0 (1) (11) (1) (101) (111) (10) ...

%e Binary to decimal rebuild S:

%e 0 1 3 1 5 7 2 ...

%Y Cf. A007088.

%K sign,base

%O 1,3

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Oct 05 2020