A081742 a(1)=1; then if n is a multiple of 3, a(n) = a(n/3) + 1; if n is not a multiple of 3 but even, a(n) = a(n/2) + 1; a(n) = a(n-1) + 1 otherwise.

1, 2, 2, 3, 4, 3, 4, 4, 3, 5, 6, 4, 5, 5, 5, 5, 6, 4, 5, 6, 5, 7, 8, 5, 6, 6, 4, 6, 7, 6, 7, 6, 7, 7, 8, 5, 6, 6, 6, 7, 8, 6, 7, 8, 6, 9, 10, 6, 7, 7, 7, 7, 8, 5, 6, 7, 6, 8, 9, 7, 8, 8, 6, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 7, 7, 8, 7, 8, 8, 5, 9, 10, 7, 8, 8, 8, 9, 10, 7, 8, 10, 8, 11, 12, 7, 8, 8, 8, 8, 9, 8

Offset: 1

Author

Benoit Cloitre, Apr 07 2003

Keywords

• nonn
• easy

Comments

A stopping problem: number of steps to reach zero starting with n and applying: x -> x/3 if x is a multiple of 3, x -> x/2 if x is even and not a multiple of 3, x -> x-1 otherwise.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

f:= proc(n) option remember;
 if n mod 3 = 0 then procname(n/3)+1
 elif n::even then procname(n/2)+1
 else procname(n-1)+1
 fi
end proc:
f(1):= 1:
map(f, [$1..200]); # Robert Israel, Apr 17 2023

Mathematica

a[n_] := a[n] = Which[n == 1, 1, Divisible[n, 3], a[n/3]+1, EvenQ[n], a[n/2]+1, True, a[n-1]+1];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, May 28 2023 *)

Formula

a(n)/log(n) is bounded.