A340717 Lexicographically earliest sequence of nonnegative integers with as many distinct values as possible such that for any n >= 0, a(rev(n)) = a(n) (where rev(n) = A030101(n) corresponds to the binary reversal of n).

0, 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 6, 4, 7, 1, 8, 5, 9, 3, 10, 6, 11, 2, 9, 6, 12, 4, 11, 7, 13, 1, 14, 8, 15, 5, 16, 9, 17, 3, 16, 10, 18, 6, 19, 11, 20, 2, 15, 9, 21, 6, 18, 12, 22, 4, 17, 11, 22, 7, 20, 13, 23, 1, 24, 14, 25, 8, 26, 15, 27, 5, 28, 16

Offset: 0

Author

Rémy Sigrist, Jan 17 2021

Keywords

• nonn
• look
• base

Comments

The condition "with as many distinct values as possible" means here that for any distinct m and n, provided the orbits of m and n under the map x -> rev(x) do not merge, then a(m) <> a(n).

Examples

			The first terms, alongside rev(n), are:
  n   a(n)  rev(n)
  --  ----  ------
   0     0       0
   1     1       1
   2     1       1
   3     2       3
   4     1       1
   5     3       5
   6     2       3
   7     4       7
   8     1       1
   9     5       9
  10     3       5
  11     6      13
  12     2       3
  13     6      11
  14     4       7
  15     7      15
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8191
• Rémy Sigrist, Colored scatterplot of the first 2^16 terms (where the color is function of A007814(n), the 2-adic valuation of n)
• Rémy Sigrist, PARI program for A340717

Crossrefs

See A340716 for similar sequences.

Cf. A000079, A005009, A005010, A007283, A007814, A020714, A030101, A340718.

Programs

PARI

See Links section.

Formula

a(2*n) = a(n).

a(n) = 1 iff n is a power of 2.

a(n) = 2 iff n belongs to A007283.

a(n) = 3 iff n belongs to A020714.

a(n) = 4 iff n belongs to A005009.

a(n) = 5 iff n belongs to A005010.

a(A340718(n)) = n (and this is the first occurrence of n in the sequence).