A360982 Order the nonnegative integers by increasing binary length of values, then by decreasing binary length of values squared, then by increasing binary length of values cubed, etc.

0, 1, 3, 2, 6, 7, 5, 4, 12, 15, 14, 13, 10, 9, 8, 11, 23, 24, 25, 27, 30, 31, 29, 28, 26, 20, 18, 17, 16, 19, 21, 22, 46, 47, 48, 50, 49, 54, 55, 59, 60, 61, 63, 62, 58, 56, 57, 52, 51, 53, 39, 40, 36, 35, 34, 32, 33, 37, 38, 42, 41, 43, 44, 45, 91, 92, 93, 94

Offset

0,3

Comments

We ignore leading zeros (and 0 is assumed to have binary length 0).

This sequence is a permutation of the nonnegative integers with inverse A360983.

The order of appearance of two distinct integers, say x and y with x > y, depends on the parity of A360963(x, y): even implies x appears before y, odd implies x appears after y.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Rémy Sigrist, Scatterplot of the first 2^15 terms

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside the binary length of their first powers, are:
  n   a(n)  w1  w2  w3  w4  w5  w6
  --  ----  --  --  --  --  --  --
   0     0   0
   1     1   1
   2     3   2   4
   3     2   2   3
   4     6   3   6   8
   5     7   3   6   9
   6     5   3   5   7  10
   7     4   3   5   7   9
   8    12   4   8  11
   9    15   4   8  12  16  20  24
  10    14   4   8  12  16  20  23
  11    13   4   8  12  15
  12    10   4   7  10  14
  13     9   4   7  10  13  16  20
  14     8   4   7  10  13  16  19
  15    11   4   7  11

Prog

(PARI) See Links section.

Crossrefs

See A360959 for a similar sequence.

Cf. A360963, A360983 (inverse).

Sequence in context: A003188 A269401 A268933 * A268831 A154435 A006042

Adjacent sequences: A360979 A360980 A360981 * A360983 A360984 A360985

Keyword

nonn,base

Author

Rémy Sigrist, Feb 27 2023

Status

approved