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%I #15 Oct 17 2023 05:12:01
%S 1,1,2,1,3,1,4,1,5,4,3,6,1,8,1,9,8,2,5,8,3,10,8,8,10,10,12,12,13,8,12,
%T 16,16,17,5,13,16,18,18,20,20,21,16,20,24,24,25,16,24,27,16,25,18,26,
%U 32,32,33,1,16,32,34,34,36,36,37,1,18,32,36,40,40,41
%N Lexicographically earliest sequence of positive terms such that for any distinct m and n, a(m) XOR (2*a(m+1)) <> a(n) XOR (2*a(n+1)) (where XOR denotes the bitwise XOR operator).
%H Rémy Sigrist, <a href="/A308059/b308059.txt">Table of n, a(n) for n = 1..10000</a>
%e The first terms, alongside a(n) XOR (2*a(n+1)), are:
%e n a(n) a(n) XOR (2*a(n+1))
%e -- ---- -------------------
%e 1 1 3
%e 2 1 5
%e 3 2 0
%e 4 1 7
%e 5 3 1
%e 6 1 9
%e 7 4 6
%e 8 1 11
%e 9 5 13
%e 10 4 2
%o (PARI) s=0; v=1; for(n=1, 72, print1(v", "); for (w=1, oo, if (!bittest(s,x=bitxor(v,2*w)), s+=2^x; v=w; break)))
%Y See A308057 and A308058 for variants.
%K nonn,look,base
%O 1,3
%A _Rémy Sigrist_, May 10 2019
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