cp's OEIS Frontend

A308059 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).

%I A308059 #15 Oct 17 2023 05:12:01
%S A308059 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 A308059 16,16,17,5,13,16,18,18,20,20,21,16,20,24,24,25,16,24,27,16,25,18,26,
%U A308059 32,32,33,1,16,32,34,34,36,36,37,1,18,32,36,40,40,41
%N A308059 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 A308059 Rémy Sigrist, <a href="/A308059/b308059.txt">Table of n, a(n) for n = 1..10000</a>
%e A308059 The first terms, alongside a(n) XOR (2*a(n+1)), are:
%e A308059   n   a(n)  a(n) XOR (2*a(n+1))
%e A308059   --  ----  -------------------
%e A308059    1     1                    3
%e A308059    2     1                    5
%e A308059    3     2                    0
%e A308059    4     1                    7
%e A308059    5     3                    1
%e A308059    6     1                    9
%e A308059    7     4                    6
%e A308059    8     1                   11
%e A308059    9     5                   13
%e A308059   10     4                    2
%o A308059 (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 A308059 See A308057 and A308058 for variants.
%K A308059 nonn,look,base
%O A308059 1,3
%A A308059 _Rémy Sigrist_, May 10 2019