A352809 -id:A352809 - cp's OEIS frontend

A353266 Inverse to A352809.

1, 2, 3, 5, 4, 7, 11, 13, 6, 9, 8, 17, 10, 19, 23, 29, 12, 31, 14, 37, 15, 41, 43, 47, 21, 33, 49, 53, 25, 59, 61, 67, 16, 69, 38, 71, 18, 73, 62, 79, 22, 83, 82, 89, 74, 97, 101, 103, 20, 107, 109, 113, 27, 127, 131, 137, 26, 121, 139, 149, 151, 157, 163, 167

Offset: 0

Rémy Sigrist, Apr 09 2022

			A352809(42) = 160, so a(160) = 42.

Rémy Sigrist, Table of n, a(n) for n = 0..10000
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A352809.

PARI
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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.

Original entry on oeis.org

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

Rémy Sigrist, Apr 04 2022

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

			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

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

Cf. A038566, A052126, A352809.

PARI
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See Links section.
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cp's OEIS Frontend

A353266 Inverse to A352809.

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