A329101 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the number of 1's in the base 4 expansion of n equals the number of 2's in the base 4 expansion of a(n).

0, 2, 1, 3, 6, 10, 8, 9, 4, 11, 5, 7, 12, 14, 13, 15, 18, 26, 22, 24, 34, 42, 38, 40, 25, 41, 27, 30, 32, 43, 33, 35, 16, 36, 17, 19, 37, 46, 39, 44, 20, 45, 21, 23, 28, 47, 29, 31, 48, 50, 49, 51, 54, 58, 56, 57, 52, 59, 53, 55, 60, 62, 61, 63, 66, 74, 70, 72

Offset: 0

Author

Rémy Sigrist, Nov 07 2019

Keywords

• nonn
• base

Comments

This sequence is a permutation of the nonnegative integers with inverse A329180.

Apparently, fixed points correspond to A001196.

The sequence has fractal features; for any k >= 0, the set of points { (n, a(n)), n = 0..4^k-1 } is symmetrical relative to the line of equation y + x = 4^k - 1 (see scatterplots in Links section).

Examples

			The first terms, alongside the base 4 representations of n and of a(n), are:
  n   a(n)  qua(n)  qua(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     2       1          2
   2     1       2          1
   3     3       3          3
   4     6      10         12
   5    10      11         22
   6     8      12         20
   7     9      13         21
   8     4      20         10
   9    11      21         23
  10     5      22         11
  11     7      23         13
  12    12      30         30
  13    14      31         32
  14    13      32         31
  15    15      33         33
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..4095
• Rémy Sigrist, PARI program for A329101
• Rémy Sigrist, Scatterplot of the sequence for n = 0..4^3-1
• Rémy Sigrist, Scatterplot of the sequence for n = 0..4^10-1
• Rémy Sigrist, Colored scatterplot of the sequence for n = 0..4^10-1 (where the color is function of A160381(n))
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A001196, A160381, A160382, A329180.

Programs

PARI

See Links section.

Formula

A160381(n) = A160382(a(n)).