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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). 3
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 (list; graph; refs; listen; history; text; internal format)
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: A116624 A248573 A125733 * A280426 A000689 A132137

Adjacent sequences:  A333552 A333553 A333554 * A333556 A333557 A333558

KEYWORD

nonn,look,base

AUTHOR

Rémy Sigrist, Mar 26 2020

STATUS

approved

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)