A333555 - OEIS

%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