initial commit

101.fs

@@ -0,0 +1,54 @@
+module _101
+
+open common
+open System
+
+let leGrange points x =
+    points
+    |> Seq.mapi (fun j (xj,y) -> 
+        y * (
+            points
+            |> Seq.mapi (fun k (xk,_) -> 
+                    if (j = k) then 1.0 else
+                    (x - xk) / (xj - xk)
+                )
+            |> Seq.fold (*) 1.0
+            )
+        )
+    |> Seq.sum
+
+let rec polynomialGen p x =
+    if p = 0 then 1L else
+    let rest = polynomialGen (p-1) x
+    let this = int64 (Math.Pow(float x, float p))
+    if p % 2 = 0 then
+        rest + this
+    else
+        rest - this
+
+let poly10 = polynomialGen 10
+
+let cube x =
+    int64 (Math.Pow(float x,3.0))
+
+let funTup f n = (n, f n)
+
+let sumOfFITsOfBOPs =
+    let leGrangeTermChecker f seqLimit =
+        [1..seqLimit]
+        |> Seq.map (fun n -> (float n, float (f n)))
+        |> (fun points -> 
+            let nth = points |> Seq.nth (seqLimit - 1) |> snd
+            let pointsMinusLast = points |> Seq.take (seqLimit - 1)
+            let nthLegrange = leGrange pointsMinusLast (float seqLimit)
+
+            (int64 nth, int64 nthLegrange)
+            )
+
+    allIntegers |> Seq.skip 2
+    |> Seq.map (leGrangeTermChecker poly10)
+    |> Seq.take 11
+    //|> Seq.takeWhile (fun (nth,nthLeGrange) ->  .Abs( nth - nthLeGrange) < 2)
+    |> Seq.toArray
+    //|> Array.map snd
+    //|> Array.sum