A244154 Permutation of natural numbers: a(0) = 1, a(1) = 2, a(2n) = A254049(a(n)), a(2n+1) = 3*a(n)-1; composition of A048673 and A005940.

1, 2, 3, 5, 4, 8, 13, 14, 6, 11, 18, 23, 25, 38, 63, 41, 7, 17, 28, 32, 39, 53, 88, 68, 61, 74, 123, 113, 172, 188, 313, 122, 9, 20, 33, 50, 46, 83, 138, 95, 72, 116, 193, 158, 270, 263, 438, 203, 85, 182, 303, 221, 424, 368, 613, 338, 666, 515, 858, 563, 1201, 938, 1563, 365, 10, 26, 43, 59, 60

Offset: 0

Author

Antti Karttunen, Jun 27 2014

Keywords

• nonn
• tabf

Comments

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

From Antti Karttunen, May 30 2017: (Start)

This sequence can be represented as a binary tree. Each left hand child is obtained by applying A254049(n) when the parent contains n, and each right hand child is obtained by applying A016789(n-1) (i.e., multiply by 3, subtract one) to the parent's contents:

1

|

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

3 5

4......../ \........8 13......../ \........14

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

6 11 18 23 25 38 63 41

7 17 28 32 39 53 88 68 61 74 123 113 172 188 313 122

etc.

This is a mirror image of the tree depicted in A245612.

(End)

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: A244153.

Cf. A005940, A048673, A054429, A243065-A243066, A243505-A243506, A245608, A245610, A245612, A016789, A254049, A285712, A285714, A286613.

Programs

Scheme

(define (A244154 n) (A048673 (A005940 (+ 1 n))))
;; Implementing a new recurrence, with memoization-macro definec:
(definec (A244154 n) (cond ((<= n 1) (+ 1 n)) ((even? n) (A254049 (A244154 (/ n 2)))) (else (+ -1 (* 3 (A244154 (/ (- n 1) 2))))))) ;; Antti Karttunen, May 30 2017

Formula

a(n) = A048673(A005940(n+1)).

From Antti Karttunen, May 30 2017: (Start)

a(0) = 1, a(1) = 2, a(2n) = A254049(a(n)), a(2n+1) = 3*a(n)-1.

a(n) = A245612(A054429(n)).

(End)