Lksim_function(k,a)
{  
# this program reports the length of the longest Lk (k-interrupted run) for k=1-5
# a is a binary sequence, k is the num. of interrups allows #
  n_length(a)
  j_0
  x_NULL
  y_NULL
for (i in 1:(n-1)){  if (a[i]!=a[i+1])
{  j_j+1
                  x[j]_i  }}
L1_matrix(0,1, j )
L2_matrix(0,1, j )
L3_matrix(0,1, j )
L4_matrix(0,1, j )
L5_matrix(0,1, j )
L_matrix(1,1, j )
if(j==0){ if(a[1]==1)
         { y[1]_n
          L[1]_n  }
        if(a[1]==0)
         { y[1]_n
          L[1]_0  }  }
if( j > 0){
y[1]_x[1]
y[j+1]_n-x[j]
if(j>1){for(j in 2:j){ y[j]_x[j]-x[j-1]}}
t_1
if(a[1]==1)
{  if((2*t+1)>(j+1)){L_y[1]}
while((2*t+1)<=(j+1))
{  s1_y[2*t-1]+y[2*t+1]
           s2_y[2*t]
L1[t]_(s1+s2)*(s2<=k)
 if((2*t+3)<=(j+1) && k>1)
       {   s21_(y[2*t+3]+s1)
                   s22_(y[2*t+2]+s2) 
L2[t]_(s21+s22)*(s22<=k)  }
   if((2*t+5)<=(j+1) && k>2)
       {   s31_(y[2*t+5]+s21)
                   s32_(y[2*t+4]+s22) 
L3[t]_(s31+s32)*(s32<=k)  }
   if((2*t+7)<=(j+1) && k>3)
       {   s41_(y[2*t+7]+s31)
                   s42_(y[2*t+6]+s32) 
L4[t]_(s41+s42)*(s42<=k)  }
   if((2*t+9)<=(j+1) && k>4)
       {   s51_(y[2*t+9]+s41)
                   s52_(y[2*t+8]+s42) 
L5[t]_(s51+s52)*(s52<=k)  }
            L[t]_max((y[2*t-1]),(y[2*t+1]),L1[t],L2[t],L3[t],L4[t],L5[t])
            t_t+1
}}
if(a[1]==0)
{ if((2*t+2)>(j+1)){L_y[2]} 
while((2*t+2)<=(j+1))
{  s1_y[2*t]+y[2*t+2]
           s2_y[2*t+1]
L1[t]_(s1+s2)*(s2<=k)
 if((2*t+4)<=(j+1) && k>1)
     {  s21_(y[2*t+4]+s1)
                s22_(y[2*t+3]+s2)
L2[t]_(s21+s22)*(s22<=k)  }
   if((2*t+6)<=(j+1) && k>2)
       {   s31_(y[2*t+6]+s21)
                   s32_(y[2*t+5]+s22) 
L3[t]_(s31+s32)*(s32<=k)  }
if((2*t+8)<=(j+1) && k>3)
       {   s41_(y[2*t+8]+s31)
                   s42_(y[2*t+7]+s32) 
L4[t]_(s41+s42)*(s42<=k)  }
if((2*t+10)<=(j+1) && k>4)
       {   s51_(y[2*t+10]+s41)
                   s52_(y[2*t+9]+s42) 
L5[t]_(s51+s52)*(s52<=k)  }
 L[t]_max((y[2*t]),(y[2*t+2]),L1[t],L2[t],L3[t],L4[t],L5[t])
           t_t+1
}}}
#result_list(y=y,a=a,L1=L1,L2=L2,L3=L3,L4=L4,L5=L5,L=L)
result_list(L1=max(L1),L2=max(L2),L3=max(L3),L4=max(L4),L5=max(L5),
L=max(L))
result
}