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

Author

Rémy Sigrist, Feb 27 2023

Keywords

• nonn
• base

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.

Examples

			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
		

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

Crossrefs

See A360959 for a similar sequence.

Cf. A360963, A360983 (inverse).

Programs

PARI

See Links section.