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.


fun ffr(n: Int) = get(n, 0)[n - 1]
 
fun ffs(n: Int) = get(0, n)[n - 1]
 
internal fun get(rSize: Int, sSize: Int): List<Int> {
    val rlist = arrayListOf(1, 3, 7)
    val slist = arrayListOf(2, 4, 5, 6)
    val list = if (rSize > 0) rlist else slist
    val targetSize = if (rSize > 0) rSize else sSize
 
    while (list.size > targetSize)
        list.removeAt(list.size - 1)
    while (list.size < targetSize) {
        val lastIndex = rlist.lastIndex
        val lastr = rlist[lastIndex]
        val r = lastr + slist[lastIndex]
        rlist += r
        var s = lastr + 1
        while (s < r && list.size < targetSize)
            slist += s++
    }
    return list
}
 
fun main(args: Array<String>) {
    print("R():")
    (1..10).forEach { print(" " + ffr(it)) }
    println()
 
    val first40R = (1..40).map { ffr(it) }
    val first960S = (1..960).map { ffs(it) }
    val indices = (1..1000).filter  { it in first40R == it in first960S }
    indices.forEach { println("Integer $it either in both or neither set") }
    println("Done")
}