A359806 Lexicographically earliest sequence of distinct positive terms such that for any n > 0 and any k > 0, floor((2^k) / n) AND floor((2^k) / a(n)) = 0 (where AND denotes the bitwise AND operator).

2, 1, 6, 5, 4, 3, 14, 9, 8, 40, 32, 24, 60, 7, 20, 17, 16, 144, 128, 15, 72, 64, 512, 12, 256, 120, 13824, 39, 2048, 35, 62, 11, 1056, 544, 30, 288, 4096, 1008, 28, 10, 1024, 156, 5504, 1408, 112, 1424, 8192, 96, 1016, 51200, 102, 240, 32768, 27648, 248, 78

Offset

1,1

Comments

In other words, for any n > 0, the binary expansions of 1/n and of 1/a(n) have no common one bit; in this sense, this sequence is similar to A238757.

This sequence is a self-inverse permutation of the positive integers.

Links

Table of n, a(n) for n=1..56.

Rémy Sigrist, C++ program

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside the binary expansions of 1/n and 1/a(n) (with periodic parts in parentheses), are:
  n   a(n)  bin(1/n)        bin(1/a(n))
  --  ----  --------------  -----------
   1     2  1.(0)           0.1(0)
   2     1  0.1(0)          1.(0)
   3     6  0.(01)          0.0(01)
   4     5  0.01(0)         0.(0011)
   5     4  0.(0011)        0.01(0)
   6     3  0.0(01)         0.(01)
   7    14  0.(001)         0.0(001)
   8     9  0.001(0)        0.(000111)
   9     8  0.(000111)      0.001(0)
  10    40  0.0(0011)       0.000(0011)
  11    32  0.(0001011101)  0.00001(0)
  12    24  0.00(01)        0.000(01)

Prog

(C++) See Links section.
(PARI) See Links section.

Crossrefs

See A306231 for a similar sequence.

Cf. A238757.

Sequence in context: A090665 A347952 A361198 * A346306 A021826 A331435

Adjacent sequences: A359803 A359804 A359805 * A359807 A359808 A359809

Keyword

nonn,base

Author

Rémy Sigrist, Jan 13 2023

Status

approved