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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.
6
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
1,2
COMMENTS
A permutation of the positive integers. See the comment at A183079.
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
EXAMPLE
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).
PROG
(Scheme, with memoizing definec-macro)
(definec (A183089 n) (cond ((<= n 1) n) ((even? n) (A050505 (A183089 (/ n 2)))) (else (A000959 (A183089 (/ (+ n 1) 2))))))
;; Antti Karttunen, May 09 2015
CROSSREFS
Inverse permutation: A257690.
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).
Sequence in context: A265901 A257801 A257726 * A191544 A191438 A191730
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Dec 24 2010
EXTENSIONS
Added a formula to the Name field and more terms, edited Example section - Antti Karttunen, May 09 2015
STATUS
approved