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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.
31
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)
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.
KEYWORD
nonn,tabf
AUTHOR
Antti Karttunen, Jul 28 2014
STATUS
approved