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A244154
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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.
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21
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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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history;
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internal format)
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OFFSET
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0,2
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COMMENTS
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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
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...................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)
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 0..8192
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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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)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,tabf,changed
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AUTHOR
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Antti Karttunen, Jun 27 2014
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STATUS
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approved
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