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A276442 Permutation of natural numbers: a(1) = 1; a(2n) = A088359(a(n)), a(2n+1) = A087686(1+a(n)), where A088359 & A087686 = numbers that occur only once & more than once in A004001. 6
1, 3, 2, 6, 7, 5, 4, 11, 14, 13, 15, 10, 12, 9, 8, 20, 26, 25, 30, 23, 29, 28, 31, 19, 24, 22, 27, 18, 21, 17, 16, 37, 47, 46, 57, 44, 56, 55, 62, 41, 53, 52, 61, 50, 60, 59, 63, 36, 45, 43, 54, 40, 51, 49, 58, 35, 42, 39, 48, 34, 38, 33, 32, 70, 85, 84, 105, 82, 104, 103, 120, 79, 101, 100, 119, 98, 118, 117, 126, 75, 95, 94 (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 A088359(n), and each right hand child as A087686(1+n), when their parent contains n:

                                    |

                 ...................1...................

                3                                       2

      6......../ \........7                   5......../ \........4

     / \                 / \                 / \                 / \

    /   \               /   \               /   \               /   \

   /     \             /     \             /     \             /     \

  11      14         13       15         10       12          9       8

20  26  25  30     23  29   28  31     19  24   22  27      18 21   17 16

etc.

As in the mirror image permutation A267112, the level k of the tree contains all numbers of binary width k like many other base-2 related permutations (A003188, A054429, A233278, etc). For a proof, see A267110, which gives the contents of each parent node (for a node containing n > 1).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8191

T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252.

Index entries for sequences related to binary expansion of n

Index entries for Hofstadter-type sequences

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(1) = 1; after which, a(2n) = A088359(a(n)), a(2n+1) = A087686(1+a(n)).

As a composition of other permutations:

a(n) = A267112(A054429(n)).

a(n) = A276344(A233278(n)).

a(n) = A276346(A233276(n)).

a(n) = A276444(A003188(n)).

PROG

(Scheme)

(definec (A276442 n) (cond ((< n 2) n) ((even? n) (A088359 (A276442 (/ n 2)))) (else (A087686 (+ 1 (A276442 (/ (- n 1) 2)))))))

CROSSREFS

Inverse: A276441.

Cf. A004001, A087686, A088359, A267110.

Related or similar permutations: A003188, A054429, A233276, A233278, A267112, A276344, A276346, A276444.

Sequence in context: A265346 A204939 A304084 * A233275 A153142 A154447

Adjacent sequences:  A276439 A276440 A276441 * A276443 A276444 A276445

KEYWORD

nonn,base,tabf

AUTHOR

Antti Karttunen, Sep 03 2016

STATUS

approved

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Last modified October 19 13:38 EDT 2018. Contains 316361 sequences. (Running on oeis4.)