A333010 Lexicographically earliest sequence of distinct positive integers such that the concatenation of the binary representations of the odd-indexed terms equals the concatenation of the binary representations of the even-indexed terms.

1, 3, 6, 2, 4, 9, 7, 14, 5, 12, 18, 10, 11, 15, 28, 19, 29, 22, 20, 36, 37, 23, 30, 13, 24, 8, 16, 33, 25, 38, 21, 44, 39, 31, 56, 17, 26, 42, 40, 34, 41, 76, 72, 35, 57, 77, 45, 46, 27, 58, 43, 59, 47, 60, 50, 80, 66, 81, 70, 82, 74, 83, 78, 84, 164, 73, 79

Offset: 1

Author

Rémy Sigrist, Mar 05 2020

Keywords

• nonn
• base

Comments

In other words, the first and second bisections have the same binary digits.

This sequence is a binary variant of A329127.

Examples

			The first terms, alongside their binary representation, are:
  n   a(n)  bin(a(n))
  --  ----  -----------------------------
   1     1  1
   2     3  11
   3     6   110
   4     2    10
   5     4      100
   6     9      1001
   7     7         111
   8    14          1110
   9     5            101
  10    12              1100
  11    18               10010
  12    10                  1010
  13    11                    1011
  14    15                      1111
  15    28                        11100
  16    19                          10011
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A333010

Crossrefs

Cf. A329127.

Programs

PARI

See Links section.