OFFSET
1,1
COMMENTS
A006577 is the number of halving and tripling steps to reach 1 in the '3x+1' problem. If n is a power of 2, a(n) = 3.
If k is a power of 2, we obtain trivial results, for example A006577(n*2^m) = A006577(2^m) + A006577(n) = m + A006577(n) => the smallest k is 1.
It appears that a(n) = 0 for n of the form 9*2^a = 9, 18, 36, 72, ...
LINKS
EXAMPLE
MAPLE
lst:={ }:C:= proc(n) a := 0 ; x := n ; while x > 1 do if type(x, 'even') then x := x/2:a:=a+1: else x := 3*x+1 ; a := a+1 ; end if; end do; a ; end proc:
for m from 0 to 40 do:lst:=lst union {2^m}:od:for n from 1 to 73 do: ii:=0:for k from 2 to 50000 while(ii=0) do:z:=n*k : if {k} intersect lst = {} and C(z)=C(n)+C(k) then ii:=1: printf ( "%d %d \n", n, k):else fi:od: if ii=0 and {n} intersect lst = {} and {k} intersect lst = {} then printf ( "%d %d \n", n, 0):else fi:od:
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 25 2013
STATUS
approved