A344792 a(n) is half the n-th term of a truncated sesquinary (base 3/2) tree.

1, 4, 2, 6, 10, 3, 13, 9, 22, 15, 121, 7, 5, 67, 20, 31, 14, 33, 76, 34, 23, 409, 182, 16, 11, 40, 8, 151, 101, 30, 46, 70, 47, 21, 49, 112, 50, 114, 172, 51, 175, 52, 35, 1381, 614, 273, 616, 24, 37, 25, 17, 60, 91, 12, 19, 340, 227, 769, 152, 45, 103, 69, 157

Offset

1,2

Comments

The tree is created by planting a tree with alternating branching and nonbranching nodes (as described in A005428). The nodes are then labeled in order -- 1,2,3,4,... All odd nodes are removed, leaving an infinite binary tree of every even number. Finally, each node is divided by two. The first four rows of the resultant tree are as follows:

1

4 2

6 10 3 13

9 22 15 121 7 5 67 20

...

The first number of the n-th row, a(2^(n-1)), is A081614(n). The last number of the n-th row is A182459(n). The lowest number of the n-th row is A061419(n). It appears that when n is even, A189706(a(n)+1) = 0, and when n is odd A189706(a(n)+1) = 1. This is true for at least the first n = 1 through 40000.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

John-Vincent Saddic, Java code to produce the first n lines of the tree

John-Vincent Saddic, Diagram to construct the tree

John-Vincent Saddic, Log/log scatterplot

Index entries for sequences that are permutations of the natural numbers

Maple

a:= proc(n) option remember;
      a(iquo(n, 2))*3 + irem(n, 2);
      while %::odd do ceil(% * 3/2) od; %/2
    end: a(1):=1:
seq(a(n), n=1..63);  # Alois P. Heinz, May 29 2021

Mathematica

a[n_] := a[n] = Module[{t}, t = a[Quotient[n, 2]]*3 + Mod[n, 2];
     While[OddQ[t], t = Ceiling[t * 3/2] ]; t/2]; a[1] = 1;
Table[a[n], {n, 1, 63}] (* Jean-François Alcover, Apr 14 2022, after Alois P. Heinz *)

Prog

(Java) See Links.
(PARI) a(n) = my(t=1); forstep(i=logint(n, 2)-1, 0, -1, t=3*t+1+bittest(n, i); my(k=valuation(t, 2)); t=(t*3^k)>>(k+1)); t; \\ Kevin Ryde, May 29 2021

Crossrefs

Inverse is A345671.

Cf. A005428, A081614, A182459, A061419, A189706.

Sequence in context: A134239 A136390 A019610 * A058613 A053227 A083760

Adjacent sequences: A344789 A344790 A344791 * A344793 A344794 A344795

Keyword

nonn,look

Author

John-Vincent Saddic, May 28 2021

Status

approved