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

0,2

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

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)

Prog

(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

Crossrefs

Inverse: A244153.

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

Sequence in context: A272090 A120255 A245608 * A182395 A244983 A059450

Adjacent sequences: A244151 A244152 A244153 * A244155 A244156 A244157

Keyword

nonn,tabf

Author

Antti Karttunen, Jun 27 2014

Status

approved