A183089 Tree generated by the lucky numbers: a(1) = 1; a(2n) = unlucky(a(n)), a(2n+1) = lucky(a(n+1)), where lucky = A000959, unlucky = A050505.

1, 2, 3, 4, 7, 5, 9, 6, 21, 11, 13, 8, 31, 14, 15, 10, 87, 29, 37, 17, 49, 19, 25, 12, 141, 42, 51, 20, 63, 22, 33, 16, 517, 112, 133, 40, 189, 50, 69, 24, 259, 64, 75, 27, 111, 35, 43, 18, 925, 177, 211, 56, 267, 66, 79, 28, 339, 83, 93, 30, 159, 45, 67, 23, 4129, 618, 685, 143, 855, 167, 201, 54, 1275, 234, 261, 65, 391, 90, 105, 34

Offset: 1

Author

Clark Kimberling, Dec 24 2010

Keywords

• nonn
• tabf

Comments

A permutation of the positive integers. See the comment at A183079.

Examples

			Top 6 levels of the binary tree:
                                     1
                                     |
                  ...................2...................
                 3                                       4
       7......../ \........5                   9......../ \........6
      / \                 / \                 / \                 / \
     /   \               /   \               /   \               /   \
    /     \             /     \             /     \             /     \
  21       11         13       8          31       14         15       10
87  29   37  17     49  19   25 12     141  42   51  20     63  22   33  16
...
From the level 3 to the level 4: 3 --> (7,5) and 4 --> (9,6).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..512
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse permutation: A257690.

Cf. A000959, A050505.

Cf. A257726 (similar permutation with a slightly different definition, resulting the first differing term at n=9, where a(9) = 21, while A257726(9) = 13), A257735 - A257738.

Cf. A183079, A237739 (other similar permutations).

Formula

Let L(n) = A000959(n), the n-th lucky number.

Let U(n) = A050505(n), the n-th unlucky numbers.

The tree-array T(n,k) is then given by rows:

T(0,0) = 1; T(1,0) = 2;

T(n,2j) = L(T(n-1),j);

T(n,2j+1) = U(T(n-1),j);

for j = 0, 1, ..., 2^(n-1) - 1, n >= 2.

a(1) = 1; a(2n) = A050505(a(n)), a(2n+1) = A000959(a(n+1)). - Antti Karttunen, May 09 2015

Extensions

Added a formula to the Name field and more terms, edited Example section - Antti Karttunen, May 09 2015