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

1,2

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..8747

Rémy Sigrist, C program for A333555

Example

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

Prog

(C) See Links section.

Crossrefs

Cf. A101274, A333556.

Sequence in context: A248573 A369414 A125733 * A352378 A280426 A000689

Adjacent sequences: A333552 A333553 A333554 * A333556 A333557 A333558

Keyword

nonn,look,base

Author

Rémy Sigrist, Mar 26 2020

Status

approved