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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A231483 A309656 A309657 * A340446 A063561 A068823

Adjacent sequences:  A296612 A296613 A296614 * A296616 A296617 A296618

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Dec 17 2017

STATUS

approved

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Last modified May 15 20:23 EDT 2021. Contains 343920 sequences. (Running on oeis4.)