A279344 a(0) = 1, a(2n) = A005187(a(n)), a(2n+1) = A055938(a(n)).

1, 2, 3, 5, 4, 6, 8, 12, 7, 9, 10, 13, 15, 17, 22, 27, 11, 14, 16, 20, 18, 21, 23, 28, 26, 30, 32, 36, 41, 45, 50, 58, 19, 24, 25, 29, 31, 33, 38, 43, 34, 37, 39, 44, 42, 48, 53, 59, 49, 55, 56, 61, 63, 65, 70, 75, 79, 84, 86, 92, 97, 103, 112, 121, 35, 40, 46, 51, 47, 52, 54, 60, 57, 62, 64, 68, 73, 77, 82, 90, 66, 69, 71, 76, 74, 80

Offset: 0

Author

Antti Karttunen, Dec 10 2016

Keywords

• nonn
• tabf

Comments

Note the indexing: the domain starts from 0, while the range excludes zero.

This sequence can be represented as a binary tree. Each left hand child is produced as A005187(n), and each right hand child as A055938(n), when the parent node contains n:

1

|

...................2...................

3 5

4......../ \........6 8......../ \........12

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

7 9 10 13 15 17 22 27

11 14 16 20 18 21 23 28 26 30 32 36 41 45 50 58

etc.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8192
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A279343.

Left edge: A256994.

Cf. A005187, A055938.

Related or similar permutations: A005940, A054429, A233276, A256997, A279339, A279342, A279347.

Programs

Scheme

(definec (A279344 n) (cond ((zero? n) 1) ((even? n) (A005187 (A279344 (/ n 2)))) (else (A055938 (A279344 (/ (- n 1) 2))))))

Formula

a(0) = 1, after which, a(2n) = A005187(a(n)), a(2n+1) = A055938(a(n)).

As a composition of other permutations:

a(n) = A279342(A054429(n)).

a(n) = A279347(A279342(n)).

a(n) = A279339(A005940(1+n)).