A279342 a(0) = 1, a(1) = 2, a(2n) = A055938(a(n)), a(2n+1) = A005187(a(n)).

1, 2, 5, 3, 12, 8, 6, 4, 27, 22, 17, 15, 13, 10, 9, 7, 58, 50, 45, 41, 36, 32, 30, 26, 28, 23, 21, 18, 20, 16, 14, 11, 121, 112, 103, 97, 92, 86, 84, 79, 75, 70, 65, 63, 61, 56, 55, 49, 59, 53, 48, 42, 44, 39, 37, 34, 43, 38, 33, 31, 29, 25, 24, 19, 248, 237, 227, 221, 210, 201, 196, 191, 187, 180, 175, 168, 171, 165, 160, 153, 154, 146, 141

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 A055938(n), and each right hand child as A005187(n), when the parent node contains n:

1

|

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

5 3

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

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

27 22 17 15 13 10 9 7

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

etc.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A279341.

Right edge: A256994.

Cf. A005187, A055938.

Related or similar permutations: A054429, A163511, A233278, A256997, A279339, A279344, A279347.

Programs

Scheme

(definec (A279342 n) (cond ((<= n 1) (+ 1 n)) ((even? n) (A055938 (A279342 (/ n 2)))) (else (A005187 (A279342 (/ (- n 1) 2))))))

Formula

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

As a composition of other permutations:

a(n) = A279344(A054429(n)).

a(n) = A279347(A279344(n)).

a(n) = A279339(A163511(n)).