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%I #14 Mar 28 2020 17:06:20
%S 1,2,4,8,5,16,32,17,64,18,37,128,19,39,72,38,30,256,20,34,66,234,512,
%T 22,41,103,174,258,60,236,1024,23,71,50,267,24,169,526,127,285,2048,
%U 28,47,187,69,378,523,272,1063,367,591,193,475,4096,31,65,176,277
%N Lexicographically earliest infinite sequence of positive terms such that for any two distinct nonempty intervals, say [t, u] and [v, w], a(t) XOR ... XOR a(u) <> a(v) XOR ... XOR a(w) (where XOR denotes the bitwise XOR operator).
%C By necessity, all terms are distincts.
%C Also, for any m and n such that m <= n, a(m) XOR ... XOR a(n) > 0.
%C This sequence has similarities with A101274; here we combine consecutive terms with the XOR operator, there with the classic addition.
%H Rémy Sigrist, <a href="/A333555/b333555.txt">Table of n, a(n) for n = 1..8747</a>
%H Rémy Sigrist, <a href="/A333555/a333555.txt">C program for A333555</a>
%e The values of a(u) XOR ... XOR a(v) for u <= v <= 10 are:
%e u\v| 1 2 3 4 5 6 7 8 9 10
%e ---+---------------------------------------
%e 1| 1 3 7 15 10 26 58 43 107 121 --> A333556(v)
%e 2| . 2 6 14 11 27 59 42 106 120
%e 3| . . 4 12 9 25 57 40 104 122
%e 4| . . . 8 13 29 61 44 108 126
%e 5| . . . . 5 21 53 36 100 118
%e 6| . . . . . 16 48 33 97 115
%e 7| . . . . . . 32 49 113 99
%e 8| . . . . . . . 17 81 67
%e 9| . . . . . . . . 64 82
%e 10| . . . . . . . . . 18
%o (C) See Links section.
%Y Cf. A101274, A333556.
%K nonn,look,base
%O 1,2
%A _Rémy Sigrist_, Mar 26 2020