A264799 Tree T generated by these rules: 0 is in T, and if x is in T, then x+1 and -2x are in T, with duplicates deleted as they occur.

0, 1, -2, 2, -4, -1, 3, 4, -8, -6, -3, 5, 8, -16, -10, -7, -5, 6, 9, 12, 16, -32, -24, -18, -15, -12, -9, 7, 10, 13, 14, 17, 20, 32, -64, -40, -34, -31, -28, -26, -23, -20, -17, -14, -11, 11, 15, 18, 21, 24, 30, 33, 36, 48, 64, -128, -96, -72, -66, -63, -60

Offset

0,3

Comments

Every integer occur in T exactly once, so that this is a permutation of the integers. Let g(0) = {0}, g(1) = {1}, g(2) = {-2,2}, g(3) = {-4,-1,3,4}, etc. The number |g(n)| of numbers in the n-th generation is a Fibonacci number except for g(3); see A264800.

Links

Clark Kimberling, Table of n, a(n) for n = 0..10000

Example

Generations begin with
    0
    1
   -2   2
   -4  -1   3   4
   -8  -6  -3   5   8
  -16 -10  -7  -5   6   9  12  16

Mathematica

z = 10; t = Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, -2*#} &, #], 1]] &, {0}, z]]; s[0] = t[[1]]; s[n_] := s[n] = Union[t[[n]], s[n - 1]];
g[n_] := Complement[s[n], s[n - 1]]; g[1] = {0};
Table[Length[g[k]], {k, 1, z}]  (* A264800 *)
u = Table[g[k], {k, 1, z}]
Flatten[u] (* A264799 *)

Crossrefs

Cf. A000045, A226080, A264800.

Sequence in context: A205843 A171727 A171942 * A248503 A359855 A214714

Adjacent sequences: A264796 A264797 A264798 * A264800 A264801 A264802

Keyword

sign,tabf,easy

Author

Clark Kimberling, Nov 25 2015

Status

approved