A245612 Permutation of natural numbers: a(0) = 1, a(1) = 2, a(2n) = 3*a(n)-1, a(2n+1) = A254049(a(n)); composition of A048673 and A163511.

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

Offset

0,2

Comments

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

From Antti Karttunen, Jul 25 2016: (Start)

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

1

|

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

5 3

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

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

41 63 38 25 23 18 11 6

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

etc.

(End)

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = A048673(A163511(n)).

a(0) = 1, a(1) = 2, a(2n) = 3*a(n)-1, a(2n+1) = A254049(a(n)). - Antti Karttunen, Jul 25 2016

Mathematica

Table[(Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ If[n == 0, 1, Prime[#] Product[Prime[m]^(Map[Ceiling[(Length@ # - 1)/2] &, DeleteCases[Split@ Join[Riffle[IntegerDigits[n, 2], 0], {0}], {k__} /; k == 1]][[-m]]), {m, #}] &[DigitCount[n, 2, 1]]], {n, 0, 63}] (* Michael De Vlieger, Jul 25 2016 *)

Prog

(Scheme) (define (A245612 n) (A048673 (A163511 n))) ;; offset 0, a(0) = 1.

Crossrefs

Inverse: A245611.

Cf. A016789, A048673, A163511, A243065-A243066, A243505-A243506, A245608, A245610, A244153, A244154, A254049.

Sequence in context: A243506 A341351 A285742 * A243066 A368316 A181921

Adjacent sequences: A245609 A245610 A245611 * A245613 A245614 A245615

Keyword

nonn,tabf

Author

Antti Karttunen, Jul 28 2014

Status

approved