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

Author

Rémy Sigrist, Dec 17 2017

Keywords

• nonn
• base

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).

Examples

			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
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Scatterplot of the first 50000 terms

Crossrefs

Cf. A000578, A175428.

Programs

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 ", "))