These two sequences of positive integers are defined as:

 







R
(
1
)



=
1
 
;
 
S
(
1
)
=
2




R
(
n
)



=
R
(
n
−
1
)
+
S
(
n
−
1
)
,

n
>
1.






{\displaystyle {\begin{aligned}R(1)&=1\ ;\ S(1)=2\\R(n)&=R(n-1)+S(n-1),\quad n>1.\end{aligned}}}




The sequence 



S
(
n
)


{\displaystyle S(n)}

 is further defined as the sequence of positive integers not present in 



R
(
n
)


{\displaystyle R(n)}

.

Sequence 



R


{\displaystyle R}

 starts:

   1, 3, 7, 12, 18, ...

Sequence 



S


{\displaystyle S}

 starts:

   2, 4, 5, 6, 8, ...



Task

 Create two functions named ffr and ffs that when given n return R(n) or S(n) respectively.
(Note that R(1) = 1 and S(1) = 2 to avoid off-by-one errors).
 No maximum value for n should be assumed.
 Calculate and show that the first ten values of R are:
 1, 3, 7, 12, 18, 26, 35, 45, 56, and 69
 Calculate and show that the first 40 values of ffr plus the first 960 values of ffs include all the integers from 1 to 1000 exactly once.


References

 Sloane's A005228 and A030124.
 Wolfram MathWorld
 Wikipedia: Hofstadter Figure-Figure sequences.


fcn genRS(reset=False){ //-->(n,R,S)
  var n=0, Rs=L(0,1), S=2;
  if(True==reset){ n=0; Rs=L(0,1); S=2; return(); }
 
  if (n==0) return(n=1,1,2);
  R:=Rs[-1] + S; Rs.append(R);
  foreach s in ([S+1..]){
     if(not Rs.holds(s)) { S=s; break; } // trimming Rs doesn't save space
  }
  return(n+=1,R,S);
}
fcn ffrs(n) { genRS(True); do(n){ n=genRS() } n[1,2] }  //-->( R(n),S(n) )