2016 Update

Task/Zeckendorf-number-representation/PowerShell/zeckendorf-number-representation-1.psh

@@ -0,0 +1,26 @@
+function Get-ZeckendorfNumber ( $N )
+    {
+    #  Calculate relevant portation of Fibonacci series
+    $Fib = @( 1, 1 )
+    While ( $Fib[-1] -lt $N ) { $Fib += $Fib[-1] + $Fib[-2] }
+
+    #  Start with 0
+    $ZeckendorfNumber = 0
+
+    #  For each number in the relevant portion of Fibonacci series
+    For ( $i = $Fib.Count - 1; $i -gt 0; $i-- )
+        {
+        #  If Fibonacci number is less than or equal to remainder of N
+        If ( $Fib[$i] -le $N )
+            {
+            #  Double Z number and add 1 (equivalent to adding a '1' to the end of a binary number)
+            $ZeckendorfNumber = $ZeckendorfNumber * 2 + 1
+            #  Reduce N by Fibonacci number, skip next Fibonacci number
+            $N -= $Fib[$i--]
+            }
+        #  If were aren't finished yet, double Z number
+        #  (equivalent to adding a '0' to the end of a binary number)
+        If ( $i ) { $ZeckendorfNumber *= 2 }
+        }
+    return $ZeckendorfNumber
+    }

Task/Zeckendorf-number-representation/PowerShell/zeckendorf-number-representation-2.psh

@@ -0,0 +1,2 @@
+#  Get Zeckendorf numbers through 20, convert to binary for display
+0..20 | ForEach { [convert]::ToString( ( Get-ZeckendorfNumber $_ ), 2 ) }