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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
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).
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.
Related or similar permutations: A003188, A054429, A233276, A233278, A267112, A276344, A276346, A276444.
Sequence in context: A265346 A204939 A304084 * A233275 A153142 A154447
KEYWORD
nonn,base,tabf
AUTHOR
Antti Karttunen, Sep 03 2016
STATUS
approved