A267106 Permutation of natural numbers: a(1) = 1, a(2n) = A080148(a(n)), a(2n+1) = A080147(a(n)).

1, 2, 3, 4, 6, 5, 7, 8, 10, 11, 13, 9, 12, 14, 16, 15, 18, 19, 24, 20, 25, 23, 29, 17, 21, 22, 26, 27, 30, 31, 35, 28, 33, 34, 40, 36, 42, 46, 53, 38, 44, 47, 55, 43, 51, 54, 62, 32, 37, 39, 45, 41, 50, 48, 57, 49, 59, 56, 65, 58, 66, 67, 74, 52, 60, 63, 70, 64, 71, 76, 82, 69, 77, 83, 87, 91, 98, 101, 112, 73, 79

Offset

1,2

Comments

This sequence can be represented as a binary tree. Each left hand child is produced as A080148(n), and each right hand child as A080147(n), when the parent node contains n:

|

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

2 3

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

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

8 10 11 13 9 12 14 16

15 18 19 24 20 25 23 29 17 21 22 26 27 30 31 35

etc.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16383

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, after which, a(2n) = A080148(a(n)), a(2n+1) = A080147(a(n)).

Prog

(Scheme, with memoization-macro definec)
(definec (A267106 n) (cond ((<= n 1) n) ((odd? n) (A080147 (A267106 (/ (- n 1) 2)))) (else (A080148 (A267106 (/ n 2))))))

Crossrefs

Inverse: A267105.

Cf. A000040, A002144, A002145, A080147, A080148.

Cf. also A267107.

Sequence in context: A361926 A332805 A332807 * A275119 A218252 A080541

Adjacent sequences: A267103 A267104 A267105 * A267107 A267108 A267109

Keyword

nonn,tabf

Author

Antti Karttunen, Feb 01 2016

Status

approved