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

Author

Rémy Sigrist, Jan 13 2023

Keywords

• nonn
• base

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.

Examples

			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)
		

Links

• Rémy Sigrist, C++ program
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A306231 for a similar sequence.

Cf. A238757.

Programs

PARI

See Links section.