def find_3smooth(k0=100000, l0=100000):
  ''' Find the next 3-smooth number after 2**k0 * 3**l0. If that
      number is 2**k * 3**l then return k,l.
  '''
  def pow(k,l):
    return 2**k * 3**l
  N0 = pow(k0,l0)
  k1,l1 = k0+1,l0
  N1 = pow(k1,l1)
  k,l = k0,l0
  while k>0:
    k -= 1
    N = pow(k,l)
    if N<N0:
      l += 1
    elif N<N1:
      N1,k1,l1 = N,k,l
  k,l = k0,l0
  while l>0:
    k += 1
    l -= 1
    N = pow(k,l)
    if N<N0:
      k += 1
    elif N<N1:
      N1,k1,l1 = N,k,l
  assert 3*N1<4*N0, "This code doesn't work for small inputs."
  return k1,l1
>>> 125743*np.log(2)-79335*np.log(3)
3.664710675366223e-06