A333555 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).

1, 2, 4, 8, 5, 16, 32, 17, 64, 18, 37, 128, 19, 39, 72, 38, 30, 256, 20, 34, 66, 234, 512, 22, 41, 103, 174, 258, 60, 236, 1024, 23, 71, 50, 267, 24, 169, 526, 127, 285, 2048, 28, 47, 187, 69, 378, 523, 272, 1063, 367, 591, 193, 475, 4096, 31, 65, 176, 277

Offset: 1

Author

Rémy Sigrist, Mar 26 2020

Keywords

• nonn
• look
• base

Comments

By necessity, all terms are distincts.

Also, for any m and n such that m <= n, a(m) XOR ... XOR a(n) > 0.

This sequence has similarities with A101274; here we combine consecutive terms with the XOR operator, there with the classic addition.

Examples

			The values of a(u) XOR ... XOR a(v) for u <= v <= 10 are:
  u\v|  1  2  3   4   5   6   7   8    9   10
  ---+---------------------------------------
    1|  1  3  7  15  10  26  58  43  107  121 --> A333556(v)
    2|  .  2  6  14  11  27  59  42  106  120
    3|  .  .  4  12   9  25  57  40  104  122
    4|  .  .  .   8  13  29  61  44  108  126
    5|  .  .  .   .   5  21  53  36  100  118
    6|  .  .  .   .   .  16  48  33   97  115
    7|  .  .  .   .   .   .  32  49  113   99
    8|  .  .  .   .   .   .   .  17   81   67
    9|  .  .  .   .   .   .   .   .   64   82
   10|  .  .  .   .   .   .   .   .    .   18
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8747
• Rémy Sigrist, C program for A333555

Crossrefs

Cf. A101274, A333556.

Programs

C

See Links section.