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).

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Rémy Sigrist, Scatterplot of the first 2^16 terms

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

Adjacent sequences: A340443 A340444 A340445 * A340447 A340448 A340449

Keyword

nonn

Author

Rémy Sigrist, Jan 07 2021

Status

approved