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

0,4

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).

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

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).

Example

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

Prog

(PARI) See Links section.

Crossrefs

See A340716 for similar sequences.

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

Sequence in context: A334867 A336159 A336473 * A336920 A365395 A366792

Adjacent sequences: A340714 A340715 A340716 * A340718 A340719 A340720

Keyword

nonn,look,base

Author

Rémy Sigrist, Jan 17 2021

Status

approved