A347272 Main diagonal of the square array A347270.

1, 1, 5, 4, 2, 8, 26, 4, 52, 1, 16, 2, 1, 16, 8, 2, 4, 8, 4, 1, 4, 1, 4, 4, 4, 1, 155, 1, 4, 2, 395, 2, 1, 2, 1, 2, 1, 4, 4, 4, 668, 1, 4, 1, 4, 2, 425, 1, 1, 4, 2, 4, 2, 850, 425, 1, 1, 2, 2, 4, 2, 4858, 2429, 1, 4, 2, 1, 2, 1, 4, 2308, 4, 3644, 1, 1, 2, 1, 1, 4, 4, 4

Offset: 0

Author

Omar E. Pol, Aug 25 2021

Keywords

• nonn

Comments

A347270 is related to the 3x + 1 (or Collatz) problem.

Conjectures from Alois P. Heinz, Aug 31 2021: (Start)

a(n) in {1, 2, 4, 5, 8, 10, 16, 26, 52, 53, 106, 155, 395, 425, 488, 668, 850, 866, 1732, 2308, 2429, 3644, 4858} for n >= 0.

a(n) in {1, 2, 4} for n >= 110. (End)

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006370, A033478, A033479, A075884, A076536, A153727, A347270, A371690 (parity).

Programs

Maple

b:= proc(n, k) option remember; `if`(k=0, n, (j->
      `if`(j::even, j/2, 3*j+1))(b(n, k-1)))
    end:
a:= n-> b(n+1, n):
seq(a(n), n=0..80);  # Alois P. Heinz, Aug 25 2021

Mathematica

b[n_, k_] := b[n, k] = If[k == 0, n, Function[j,
     If[EvenQ[j], j/2, 3*j + 1]][b[n, k - 1]]];
a[n_] := b[n + 1, n];
Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Apr 07 2022, after Alois P. Heinz *)