A266418 Permutation of natural numbers: a(1) = 1, a(2n) = A266410(a(n)), a(2n+1) = A266409(1+a(n)).

1, 4, 2, 10, 6, 7, 3, 22, 20, 15, 11, 16, 12, 9, 5, 40, 53, 37, 45, 29, 33, 24, 21, 31, 35, 25, 23, 19, 18, 13, 8, 68, 111, 85, 156, 64, 104, 75, 123, 51, 74, 56, 87, 43, 59, 39, 48, 54, 80, 61, 90, 46, 60, 42, 57, 36, 44, 34, 41, 27, 26, 17, 14, 107, 210, 167, 387, 133, 276, 229, 573, 101, 198, 158, 351, 120

Offset

1,2

Comments

This sequence can be represented as a binary tree. Each left hand child is produced as A266410(n), and each right hand child as A266409(1+n), when the parent node contains n:

|

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

4 2

10......../ \........6 7......../ \........3

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

22 20 15 11 16 12 9 5

40 53 37 45 29 33 24 21 31 35 25 23 19 18 13 8

etc.

Links

Antti Karttunen, Table of n, a(n) for n = 1..4095

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, after which: a(2n) = A266410(a(n)), a(2n+1) = A266409(1+a(n)).

As a composition of related permutations:

a(n) = A266638(A237126(n)).

Prog

(Scheme, with memoization-macro definec)
(definec (A266418 n) (cond ((<= n 1) n) ((even? n) (A266410 (A266418 (/ n 2)))) (else (A266409 (+ 1 (A266418 (/ (- n 1) 2)))))))

Crossrefs

Inverse: A266417.

Cf. A266409, A266410.

Similar or related permutations: A237126, A266638.

Sequence in context: A283938 A283943 A283942 * A193422 A357595 A160572

Adjacent sequences: A266415 A266416 A266417 * A266419 A266420 A266421

Keyword

nonn,tabf

Author

Antti Karttunen, Jan 28 2016

Status

approved