A296615 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, a(n) XOR a(n+1) is a cube (where XOR denotes the XOR binary operator).

1, 9, 8, 19, 18, 26, 27, 91, 38, 39, 47, 46, 53, 52, 60, 61, 64, 65, 73, 72, 83, 82, 90, 130, 131, 139, 138, 145, 144, 152, 153, 217, 164, 124, 103, 102, 110, 111, 116, 117, 125, 165, 173, 172, 183, 182, 190, 191, 194, 195, 203, 202, 209, 208, 216, 399, 343

Offset

1,2

Comments

This sequence has similarities with A175428: here a(n) XOR a(n+1) is a cube, there a(n) + a(n+1) is a cube.

This sequence is conjectured to the a permutation of the natural numbers.

The first fixed points are: 1, 5676, 5677, 5698, 11677, 13226, 26943, 26946, 27575, 28039, 28569, 28625, 30127, 30162, 37660, 37661, 44672, 44673, 45934.

The scatterplot of the first terms of the sequence shows hatches (see Links section).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Scatterplot of the first 50000 terms

Example

The first terms, alongside a(n) XOR a(n+1), are:
  n     a(n)    a(n) XOR a(n+1)
  --    ----    ---------------
   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    5^3
   9      38    1^3
  10      39    2^3
  11      47    1^3
  12      46    3^3
  13      53    1^3
  14      52    2^3
  15      60    1^3
  16      61    5^3
  17      64    1^3
  18      65    2^3
  19      73    1^3
  20      72    3^3

Prog

(PARI) seen = 0; unseen = 1
other(p) = seen += 2^p; while (bittest(seen, unseen), unseen++); \
for (v=unseen, oo, if (!bittest(seen, v) && ispower(bitxor(p, v), 3), return (v)))
for (n=1, 57, v=if (n==1, 1, other(v)); print1 (v ", "))

Crossrefs

Cf. A000578, A175428.

Sequence in context: A370882 A363327 A309657 * A340446 A063561 A068823

Adjacent sequences: A296612 A296613 A296614 * A296616 A296617 A296618

Keyword

nonn,base

Author

Rémy Sigrist, Dec 17 2017

Status

approved