A352812 Lexicographically earliest sequence of distinct nonnegative integers such that for any n and k coprime the binary expansions of a(n) and a(k) have no common 1's.

0, 1, 2, 4, 8, 3, 16, 5, 32, 9, 64, 6, 128, 17, 10, 256, 512, 7, 1024, 12, 18, 65, 2048, 33, 4096, 129, 34, 20, 8192, 11, 16384, 257, 66, 260, 24, 35, 32768, 261, 130, 13, 65536, 19, 131072, 68, 40, 2049, 262144, 36, 524288, 264, 514, 132, 1048576, 37, 72, 21

Offset

1,3

Comments

The n-th row of A038566 gives the k's to consider when computing a(n).

Links

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

Rémy Sigrist, Colored logarithmic scatterplot of the first 10000 terms (where the color is function of A052126(n))

Rémy Sigrist, PARI program

Example

The first terms, alongside their binary expansion, the corresponding k's and the implied forbidden bits, are:
  n   a(n)  bin(a(n))  k's                              bin(forbidden)
  --  ----  ---------  -------------------------------  --------------
   1     0          0  {1}                                           0
   2     1          1  {1}                                           0
   3     2         10  {1, 2}                                        1
   4     4        100  {1, 3}                                       10
   5     8       1000  {1, 2, 3, 4}                                111
   6     3         11  {1, 5}                                     1000
   7    16      10000  {1, 2, 3, 4, 5, 6}                         1111
   8     5        101  {1, 3, 5, 7}                              11010
   9    32     100000  {1, 2, 4, 5, 7, 8}                        11101
  10     9       1001  {1, 3, 7, 9}                             110010
  11    64    1000000  {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}          111111
  12     6        110  {1, 5, 7, 11}                           1011000

Prog

(PARI) See Links section.

Crossrefs

Cf. A038566, A052126, A352809.

Sequence in context: A109588 A254788 A347669 * A052331 A242365 A119436

Adjacent sequences: A352809 A352810 A352811 * A352813 A352814 A352815

Keyword

nonn,base

Author

Rémy Sigrist, Apr 04 2022

Status

approved