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

0,2

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).

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

Formula

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A001196, A160381, A160382, A329180.

Sequence in context: A086964 A076242 A066203 * A024866 A076058 A098124

Adjacent sequences: A329098 A329099 A329100 * A329102 A329103 A329104

Keyword

nonn,base

Author

Rémy Sigrist, Nov 07 2019

Status

approved