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

Author

Rémy Sigrist, Apr 04 2022

Keywords

• nonn
• base

Comments

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

Examples

			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
		

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

Crossrefs

Cf. A038566, A052126, A352809.

Programs

PARI

See Links section.