A081742 - OEIS

%I #19 May 28 2023 08:45:31

%S 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,

%T 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,

%U 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

%N 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.

%C 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.

%H Robert Israel, <a href="/A081742/b081742.txt">Table of n, a(n) for n = 1..10000</a>

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

%p f:= proc(n) option remember;

%p  if n mod 3 = 0 then procname(n/3)+1

%p  elif n::even then procname(n/2)+1

%p  else procname(n-1)+1

%p  fi

%p end proc:

%p f(1):= 1:

%p map(f, [$1..200]); # _Robert Israel_, Apr 17 2023

%t 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];

%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, May 28 2023 *)

%K nonn,easy

%O 1,2

%A _Benoit Cloitre_, Apr 07 2003