Data commit

Task/Kaprekar-numbers/F-Sharp/kaprekar-numbers.fs

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+// Count digits in number
+let digits x =
+    let rec digits' p x =
+        if 10.**p > x then p else digits' (p + 1.) x
+    digits' 1. x
+
+
+// Is n a Kaprekar number?
+let isKaprekar n =
+    // Reference: http://oeis.org/A006886
+    // Positive numbers n such that n=q+r
+    // And n^2=q*10^m+r,
+    //  for some m >= 1,
+    //  q>=0 and 0<=r<10^m,
+    //  with n != 10^a, a>=1.
+    let nSquared = n * n
+    let a = float((digits n) - 1.)
+
+    // Create a list of tuples from the nSquared digit splits
+    [1. .. float (digits nSquared)]
+    |> List.map (fun e ->
+        // Splits the nSquared digits into 2 parts
+        let x = 10.**e
+        let q = float(int(Math.Floor (nSquared / x)))
+        let r = nSquared - (q * x)
+        (q, r))
+    // Filter results based on rules
+    |> List.exists (fun (q, r) ->
+        q + r = n &&
+        if a >= 1. then n % 10.**a <> 0. else true)
+
+
+// List Kaprekar numbers from 1 to 10,000
+[1 .. 10000]
+|> List.filter (float >> isKaprekar)