A340717 - OEIS

%I #11 Jan 22 2021 14:18:42

%S 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,

%T 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,

%U 11,22,7,20,13,23,1,24,14,25,8,26,15,27,5,28,16

%N 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).

%C 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).

%H Rémy Sigrist, <a href="/A340717/b340717.txt">Table of n, a(n) for n = 0..8191</a>

%H Rémy Sigrist, <a href="/A340717/a340717.png">Colored scatterplot of the first 2^16 terms</a> (where the color is function of A007814(n), the 2-adic valuation of n)

%H Rémy Sigrist, <a href="/A340717/a340717.gp.txt">PARI program for A340717</a>

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

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

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

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

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

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

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

%e The first terms, alongside rev(n), are:

%e   n   a(n)  rev(n)

%e   --  ----  ------

%e    0     0       0

%e    1     1       1

%e    2     1       1

%e    3     2       3

%e    4     1       1

%e    5     3       5

%e    6     2       3

%e    7     4       7

%e    8     1       1

%e    9     5       9

%e   10     3       5

%e   11     6      13

%e   12     2       3

%e   13     6      11

%e   14     4       7

%e   15     7      15

%o (PARI) See Links section.

%Y See A340716 for similar sequences.

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

%K nonn,look,base

%O 0,4

%A _Rémy Sigrist_, Jan 17 2021