2016 Update

Task/Ludic-numbers/PowerShell/ludic-numbers-1.psh

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+#  Start with a pool large enough to meet the requirements
+$Pool = [System.Collections.ArrayList]( 2..22000 )
+
+#  Start with 1, because it's grandfathered in
+$Ludic = @( 1 )
+
+#  While the size of the pool is still larger than the next Ludic number...
+While ( $Pool.Count -gt $Pool[0] )
+    {
+    #  Add the next Ludic number to the list
+    $Ludic += $Pool[0]
+
+    #  Remove from the pool all entries whose index is a multiple of the next Ludic number
+    [math]::Truncate( ( $Pool.Count - 1 )/ $Pool[0])..0 | ForEach { $Pool.RemoveAt( $_ * $Pool[0] ) }
+    }
+
+#  Add the rest of the numbers in the pool to the list of Ludic numbers
+$Ludic += $Pool.ToArray()

Task/Ludic-numbers/PowerShell/ludic-numbers-2.psh

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+#  Display the first 25 Ludic numbers
+$Ludic[0..24] -join ", "
+''
+
+#  Display the count of all Ludic numbers under 1000
+$Ludic.Where{ $_ -le 1000 }.Count
+''
+
+#  Display the 2000th through the 2005th Ludic number
+$Ludic[1999..2004] -join ", "
+''
+
+#  Display all Ludic triplets less than 250
+$TripletStart = $Ludic.Where{ $_ -lt 244 -and ( $_ + 2 ) -in $Ludic -and ( $_ + 6 ) -in $Ludic }
+$TripletStart.ForEach{ $_, ( $_ + 2 ), ( $_ + 6 ) -join ", " }