

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.


21



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
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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(n1) (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 memoizationmacro 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, A243065A243066, A243505A243506, A245612, 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



