This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A267112 Permutation of natural numbers: a(1) = 1; a(2n) = A087686(1+a(n)), a(2n+1) = A088359(a(n)), where A088359 and A087686 = numbers that occur only once (resp. more than once) in A004001. 13
 1, 2, 3, 4, 5, 7, 6, 8, 9, 12, 10, 15, 13, 14, 11, 16, 17, 21, 18, 27, 22, 24, 19, 31, 28, 29, 23, 30, 25, 26, 20, 32, 33, 38, 34, 48, 39, 42, 35, 58, 49, 51, 40, 54, 43, 45, 36, 63, 59, 60, 50, 61, 52, 53, 41, 62, 55, 56, 44, 57, 46, 47, 37, 64, 65, 71, 66, 86, 72, 76, 67, 106, 87, 90, 73, 96, 77, 80, 68, 121, 107, 109, 88 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence can be represented as a binary tree. Each left hand child is produced as A087686(1+n), and each right hand child as A088359(n), when their parent contains n:                                     |                  ...................1...................                 2                                       3       4......../ \........5                   7......../ \........6      / \                 / \                 / \                 / \     /   \               /   \               /   \               /   \    /     \             /     \             /     \             /     \   8       9          12       10         15       13         14       11 16 17   21 18      27  22   24  19     31  28   29  23     30  25   26  20 etc. The level k of the tree contains all numbers of binary width k, like many base-2 related permutations (A003188, A054429, etc). For a proof, see A267110, which gives the contents of each parent node (for node containing n). A276442 shows the mirror-image of the same tree. LINKS Antti Karttunen, Table of n, a(n) for n = 1..8192 T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252. FORMULA a(1) = 1; after which, a(2n) = A087686(1+a(n)), a(2n+1) = A088359(a(n)). As a composition of other permutations: a(n) = A276442(A054429(n)). a(n) = A276344(A233276(n)). a(n) = A276346(A233278(n)). a(n) = A276446(A003188(n)). Other identities. For all n >= 0: a(2^n) = 2^n. [Follows from the properties (3) and (4) of A004001 given on page 227 of Kubo & Vakil paper.] a(A000225(n)) = A006127(n), i.e., a((2^(n+1)) - 1) = 2^n + n. [Numbers at the right edge.] PROG (Scheme, with memoization-macro definec) (definec (A267112 n) (cond ((< n 2) n) ((even? n) (A087686 (+ 1 (A267112 (/ n 2))))) (else (A088359 (A267112 (/ (- n 1) 2)))))) CROSSREFS Inverse: A267111. Cf. A000079, A000225, A004001, A006127, A087686, A088359, A267110. Similar or related permutations: A003188, A054429, A276442, A233276, A233278, A276344, A276346, A276446. Cf. also permutations A266411, A266412 and arrays A265901, A265903. Sequence in context: A161919 A269391 A095903 * A269392 A166277 A145342 Adjacent sequences:  A267109 A267110 A267111 * A267113 A267114 A267115 KEYWORD nonn,tabf,look AUTHOR Antti Karttunen, Jan 10 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 19 23:44 EDT 2019. Contains 328244 sequences. (Running on oeis4.)