A302544 Lexicographically earliest sequence of distinct nonnegative numbers such that for any n >= 0, A065359(a(n)) = - A065359(n).

0, 2, 1, 3, 8, 10, 6, 11, 4, 9, 5, 7, 12, 14, 13, 15, 26, 34, 18, 32, 40, 42, 35, 43, 24, 38, 16, 27, 41, 46, 30, 44, 19, 33, 17, 22, 36, 47, 25, 39, 20, 28, 21, 23, 31, 45, 29, 37, 48, 50, 49, 51, 56, 58, 54, 59, 52, 57, 53, 55, 60, 62, 61, 63, 74, 106, 66

Offset

0,2

Comments

This sequence is a self-inverse permutation of the nonnegative numbers, with fixed points A039004.

We can build an analog of this sequence for any base b > 1 by considering the alternating sum of digits in base b instead of A065359.

This sequence has similarities with A298847.

The scatter plots have an interesting, "fibrous" look. - Antti Karttunen, Jul 21 2018

Links

Rémy Sigrist, Table of n, a(n) for n = 0..16384

Rémy Sigrist, Colored scatterplot of the first 2^16 terms (where the color is function of A065359(n))

Rémy Sigrist, Scatterplot of the first 3^10 terms of the base 3 analog of this sequence

Rémy Sigrist, Scatterplot of the first 4^10 terms of the base 4 analog of this sequence

Rémy Sigrist, Scatterplot of the first 10^6 terms of the base 10 analog of this sequence

Rémy Sigrist, Scatterplot of the first 10!/2 terms of the factorial base analog of this sequence

Rémy Sigrist, C++ program for A302544

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside the binary representations of n and of a(n), and A065359(n), are:
  n   a(n)  bin(n)  bin(a(n))  A065359(n)
  --  ----  ------  ---------  ----------
   0     0       0       0      0
   1     2       1      10      1
   2     1      10       1     -1
   3     3      11      11      0
   4     8     100    1000      1
   5    10     101    1010      2
   6     6     110     110      0
   7    11     111    1011      1
   8     4    1000     100     -1
   9     9    1001    1001      0
  10     5    1010     101     -2
  11     7    1011     111     -1
  12    12    1100    1100      0
  13    14    1101    1110      1
  14    13    1110    1101     -1
  15    15    1111    1111      0
  16    26   10000   11010      1
  17    34   10001  100010      2
  18    18   10010   10010      0
  19    32   10011  100000      1
  20    40   10100  101000      2

Prog

(C++) See Links section.

Crossrefs

Cf. A039004 (fixed points), A065359, A298847.

Sequence in context: A342224 A145490 A329180 * A057300 A076655 A236438

Adjacent sequences: A302541 A302542 A302543 * A302545 A302546 A302547

Keyword

nonn,look,base

Author

Rémy Sigrist, Apr 09 2018

Status

approved