EKG sequence convergence: Difference between revisions

Two EKG generators with differing starts can converge to produce the same sequence after initial differences.<br>

<code>EKG(N1)</code> and <code>EKG(N2)</code> are said to to have converged at and after generation <code>a(c)</code> ıf the set (unordered collectıon of ıtems) of digıts used so far by <code>EKG(N1)</code> and <code>EKG(N2)</code> are equal and <code>a(c)</code> ıs the same for both.

;Extra Credıt:

Fınd the position ın sequence <code>EKG(2)</code> of the 10000th prıme number 104729

=={{header|F_Sharp|F#}}==

===The Function===

<lang fsharp>

// Generate EKG Sequences. Nigel Galloway: October 6th., 2017

let EKG n=seq{

let fN,fG=let i=System.Collections.Generic.Dictionary<int,int>()

let fN g=(if not (i.ContainsKey g) then i.[g]<-g);(g,i.[g])

((fun e->i.[e]<-i.[e]+e), (fun l->l|>List.map fN))

let fU l= pCache|>Seq.takeWhile(fun n->n<=l)|>Seq.filter(fun n->l%n=0)|>List.ofSeq

let rec EKG l (α,β)=seq{let b=fU β in if (β=n||β<snd((fG b|>List.maxBy snd))) then fN α; yield! EKG l (fG l|>List.minBy snd)

else fN α;yield β;yield! EKG b (fG b|>List.minBy snd)}

yield! seq[1;n]; let g=fU n in yield! EKG g (fG g|>Seq.minBy snd)}

</lang>

===The Task===

<lang fsharp>

EKG 2 |> Seq.take 45 |> Seq.iter(printf "%2d, ")

let EKGconv n g=Seq.zip(EKG n)(EKG g)|>Seq.skip 2|>Seq.scan(fun(n,i,g,e)(l,β)->(Set.add l n,Set.add β i,l,β))(set[1;n],set[1;g],0,0)|>Seq.takeWhile(fun(n,i,g,e)->g<>e||n<>i)

printfn "%d" (let n,_,_,_=EKGconv 2 5|>Seq.last in ((Set.count n)+1)

</lang>

{{out}}

<pre>

45

</pre>

===Extra Credit===

<lang fsharp>

prıntfn "%d" (EKG 2|>Seq.takeWhile(fun n->n<>104729) ((Seq.length n)+1)

</lang>

{{out}}

<pre>

203786

</pre>