A268712 Permutation of natural numbers: a(1) = 1, a(2n) = A268677(a(n)), a(2n+1) = A268678(1+a(n)).

1, 2, 3, 6, 4, 9, 5, 13, 11, 10, 7, 21, 18, 12, 8, 29, 23, 25, 20, 24, 19, 14, 15, 45, 40, 39, 34, 28, 22, 17, 16, 62, 56, 49, 42, 54, 48, 44, 37, 51, 47, 43, 36, 30, 26, 33, 27, 95, 87, 84, 75, 80, 74, 73, 65, 61, 53, 46, 41, 38, 32, 35, 31, 129, 120, 115, 108, 100, 93, 88, 82, 112, 105, 99, 92, 94, 86, 78, 70

Offset

1,2

Comments

This sequence can be represented as a binary tree. Each left hand child is produced as A268677(n), and each right hand child as A268678(1+n), when the parent node contains n:

|

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

2 3

6......../ \........4 9......../ \........5

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

13 11 10 7 21 18 12 8

29 23 25 20 24 19 14 15 45 40 39 34 28 22 17 16

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) = A268677(a(n)), a(2n+1) = A268678(1+a(n)).

Prog

(Scheme, with memoization-macro definec)
(definec (A268712 n) (cond ((= 1 n) n) ((even? n) (A268677 (A268712 (/ n 2)))) (else (A268678 (+ 1 (A268712 (/ (- n 1) 2)))))))

Crossrefs

Inverse: A268711.

Cf. A268677, A268678.

Sequence in context: A101369 A125147 A103864 * A152679 A232561 A348395

Adjacent sequences: A268709 A268710 A268711 * A268713 A268714 A268715

Keyword

nonn,tabf

Author

Antti Karttunen, Feb 11 2016

Status

approved