A166549 The number of halving steps of the Collatz 3x+1 map to reach 1 starting from 2n-1.

0, 5, 4, 11, 13, 10, 7, 12, 9, 14, 6, 11, 16, 70, 13, 67, 18, 10, 15, 23, 69, 20, 12, 66, 17, 17, 9, 71, 22, 22, 14, 68, 19, 19, 11, 65, 73, 11, 16, 24, 16, 70, 8, 21, 21, 59, 13, 67, 75, 18, 18, 56, 26, 64, 72, 45, 10, 23, 15, 23, 61, 31, 69, 31, 77, 20, 20, 28, 58, 28, 12, 66, 74, 74, 17

Offset: 1

Author

Jimin Park, Oct 16 2009

Keywords

• nonn

Comments

A given term k appears A131450(k) times. - Flávio V. Fernandes, Mar 13 2022

Links

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

Crossrefs

Cf. A131450, A006577, A075680.

Programs

Maple

A006370 := proc(n) if type(n,'even') then n/2; else 3*n+1 ; end if; end proc:
A006577 := proc(n) a := 0 ; x := n ; while x > 1 do x := A006370(x) ; a := a+1 ; end do; a ; end proc:
A006667 := proc(n) a := 0 ; x := n ; while x > 1 do if type(x,'even') then x := x/2 ; else x := 3*x+1 ; a := a+1 ; end if; end do; a ; end proc:
A075680 := proc(n) A006667(2*n-1) ; end proc:
A166549 := proc(n) A006577(2*n-1)-A075680(n) ; end: seq(A166549(n),n=1..120) ; # R. J. Mathar, Oct 18 2009
# second Maple program:
b:= proc(n) option remember; `if`(n=1, 0,
      1+b(`if`(n::even, n/2, (3*n+1)/2)))
    end:
a:= n-> b(2*n-1):
seq(a(n), n=1..75);  # Alois P. Heinz, Mar 14 2022

Mathematica

b[n_] := b[n] = If[n == 1, 0, 1 + b[If[EvenQ[n], n/2, (3n+1)/2]]];
a[n_] := b[2n-1];
Table[a[n], {n, 1, 75}] (* Jean-François Alcover, Apr 22 2022, after Alois P. Heinz *)

Formula

a(n) = A006577(2n-1) - A075680(n).

Extensions

Edited and extended by R. J. Mathar, Oct 18 2009