A338047 Lexicographically earliest sequence of nonnegative integers such that for any n >= 0, a(n) does not appear in the XOR-triangle with bottom row (a(0), ..., a(n-1)).

0, 1, 2, 4, 8, 9, 11, 16, 17, 18, 21, 22, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 48, 52, 64, 65, 66, 68, 69, 72, 73, 75, 77, 79, 80, 81, 82, 85, 92, 93, 95, 98, 126, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 140, 142, 143, 144, 145, 147

Offset

0,3

Comments

All powers of 2 appear in the sequence.

Links

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

Rémy Sigrist, PARI program for A338047

Example

The first terms, alongside the corresponding XOR-triangle, are:
                                            6
                                        2       4
                                   17      19      23
                               29      12      31       8
                            1      28      16      15       7
                        0       1      29      13       2       5
                    8       8       9      20      25      27      30
                 7     15       7      14      26       3      24      6
              2     5      10      13       3      25      26       2      4
           1     3      6      12       1       2      27       1      3      7
  a(n)| 0     1     2       4       8       9      11      16      17     18     21
  ----+----------------------------------------------------------------------------
  n   | 0     1     2       3       4       5       6       7       8      9     10

Prog

(PARI) See Links section.

Crossrefs

Cf. A001651 (additive analog), A003987.

Sequence in context: A190723 A010071 A035271 * A243186 A326673 A297126

Adjacent sequences: A338044 A338045 A338046 * A338048 A338049 A338050

Keyword

nonn,base

Author

Rémy Sigrist, Oct 08 2020

Status

approved