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A340446
Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) XOR a(n+1) is a positive cube as small as possible (where XOR denotes the bitwise XOR operator).
2
0, 1, 9, 8, 19, 18, 26, 27, 91, 90, 82, 83, 72, 73, 65, 64, 61, 60, 52, 53, 46, 47, 39, 38, 102, 103, 111, 110, 117, 116, 124, 125, 165, 164, 172, 173, 182, 183, 191, 190, 254, 255, 247, 246, 237, 236, 228, 229, 152, 153, 145, 144, 139, 138, 130, 131, 195, 194
OFFSET
0,3
COMMENTS
This sequence appears to be a permutation of the nonnegative integers.
EXAMPLE
The first terms, alongside a(n) XOR a(n+1), are:
n a(n) a(n) XOR a(n+1)
-- ---- ---------------
0 0 1^3
1 1 2^3
2 9 1^3
3 8 3^3
4 19 1^3
5 18 2^3
6 26 1^3
7 27 4^3
8 91 1^3
9 90 2^3
10 82 1^3
11 83 3^3
12 72 1^3
13 73 2^3
14 65 1^3
15 64 5^3
PROG
(PARI) s=0; v=0; for (n=0, 57, print1 (v", "); s+=2^v; for (k=1, oo, if (!bittest(s, w=bitxor(v, k^3)), v=w; break)))
CROSSREFS
See A340406 for similar sequences.
Cf. A000578.
Sequence in context: A363327 A309657 A296615 * A063561 A068823 A264301
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jan 07 2021
STATUS
approved