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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). 3
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 (list; graph; refs; listen; history; text; internal format)
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 A336933 A336460

Adjacent sequences:  A340714 A340715 A340716 * A340718 A340719 A340720

KEYWORD

nonn,look,base

AUTHOR

Rémy Sigrist, Jan 17 2021

STATUS

approved

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Last modified August 8 09:40 EDT 2022. Contains 356009 sequences. (Running on oeis4.)