A367262 - OEIS

A367262

Lexicographically earliest sequence of distinct nonnegative integers such that the values a(0) XOR ... XOR a(k) (for some k >= 0) are all distinct (where XOR denotes the bitwise XOR operator).

0, 1, 2, 4, 3, 6, 7, 8, 5, 14, 9, 16, 10, 11, 12, 15, 13, 25, 17, 18, 19, 21, 22, 20, 24, 29, 23, 32, 26, 27, 28, 30, 31, 49, 33, 35, 34, 37, 38, 41, 40, 36, 44, 64, 39, 42, 43, 45, 46, 47, 48, 50, 51, 52, 54, 53, 56, 55, 59, 57, 60, 58, 66, 65, 69, 67, 61, 96

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OFFSET

0,3

COMMENTS

This sequence is a variant of A333400; here we combine initial terms with the XOR operator, there with the addition.

This sequence is well defined; after some initial terms we can extend the sequence with a power of 2 greater that any prior term or even a smaller value.

This sequence is a permutation of the nonnegative integers (with inverse A367263):

- for any k >= 0, the least value >= 2^k is precisely 2^k,

- all powers of 2 appear in the sequence,

- after a power of 2, if the least value not yet in the sequence is less than this power of 2, then this value will be the next term.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, C++ program

Index entries for sequences that are permutations of the natural numbers

EXAMPLE

The first terms are:

n a(n) a(0) XOR ... XOR a(n)

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