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 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

%I

%S 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,

%T 74,123,113,172,188,313,122,9,20,33,50,46,83,138,95,72,116,193,158,

%U 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

%N 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.

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

%C From _Antti Karttunen_, May 30 2017: (Start)

%C 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:

%C 1

%C |

%C ...................2...................

%C 3 5

%C 4......../ \........8 13......../ \........14

%C / \ / \ / \ / \

%C / \ / \ / \ / \

%C / \ / \ / \ / \

%C 6 11 18 23 25 38 63 41

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

%C etc.

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

%C (End)

%H Antti Karttunen, <a href="/A244154/b244154.txt">Table of n, a(n) for n = 0..8192</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

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

%F From _Antti Karttunen_, May 30 2017: (Start)

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

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

%F (End)

%o (Scheme)

%o (define (A244154 n) (A048673 (A005940 (+ 1 n))))

%o ;; Implementing a new recurrence, with memoization-macro definec:

%o (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

%Y Inverse: A244153.

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

%K nonn,tabf

%O 0,2

%A _Antti Karttunen_, Jun 27 2014

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Last modified January 27 04:57 EST 2020. Contains 331291 sequences. (Running on oeis4.)