A Ruby routine to generate Kaprekar numbers

What are Kaprekar numbers ?
Kaprekar numbers are special numbers that were discovered by India mathematician Dattaraya Ramchandra Kaprekar. A more detailed explanation of Kaprekar and his numbers can be found here
http://en.wikipedia.org/wiki/Kaprekar_number
http://en.wikipedia.org/wiki/D._R._Kaprekar
This is a humble effort from my side to pay tribute to this great mathematician. Here is a Ruby routine to generate "n" Kaprekar numbers...

	#!/usr/bin/ruby
	=begin
	A Ruby routine to generate Kaprekar's numbers
	Don't confuse with Kaperkar's constant - 6174
	=end
	require 'optparse'
	require 'ostruct'
	class C_args
	def initialize (arguments)
	@m_ostruct = OpenStruct.new
	@m_optparser = OptionParser.new
	@m_args = arguments
	end
	def parse
	@m_optparser.banner = "Usage: ./generate_kaprekar.rb -n <integer number>"
	@m_optparser.on("-n VAL", Integer, "Range for kaprekar numbers") do |val|
	@m_ostruct.num = val
	end
	@m_optparser.parse(@m_args)
	if @m_args.empty?
	puts @m_optparser
	exit
	end
	return @m_ostruct
	end
	end
	class C_gen_kaprekar
	def initialize (number)
	@number = number
	end
	def gen_kaprekar()
	puts "Number -> #{@number}"
	for i in 2..@number
	n_square = i**2
	s_square = n_square.to_s
	s_size = n_square.to_s.size
	if (s_size % 2 == 0)
	j = (s_size / 2)
	k = (s_size / 2)
	else
	j = (s_size + 1) / 2
	k = ((s_size + 1) / 2) - 1
	end
	s_n1 = s_square[0,k]
	s_n2 = s_square[k,j]
	i_n2 = s_n2.to_i
	i_n1 = s_n1.to_i
	if (i == i_n1 + i_n2)
	puts "Kaprekar -> #{i}"
	end
	end
	end
	end
	h_c_args = C_args.new(ARGV)
	m1_ostruct= h_c_args.parse
	puts "number limit = #{m1_ostruct.num}"
	h_c_gen_kaprekar = C_gen_kaprekar.new(m1_ostruct.num)
	h_c_gen_kaprekar.gen_kaprekar

view raw generate_kaprekar.rb hosted with ❤ by GitHub

The output might look something like this...

On the mathematics of verification

Many of you would wonder why I am writing after more than 3 years. My last post was way back in 2010. Well I am still in the business of ASIC verification.  These years had been immensely profound and educating. When you get a glimpse of infinity, all our lifetime's learning appear to be a drop of water in the ocean.

But the quest for knowledge still goes on. I may not be able to ever understand the workings of this universe, but I still want to pursue the quest, even if it is for the mundane.

So in continuation to my last post "on the mathematics of assertions", I have got some really concrete insight into the problem from a much broader perspective. The problem of verification is far more complex than we perceive through dynamic simulations. There is a profound mathematical basis for the behavior of complex boolean systems. I have got a hold on the mathematics, but there is lot of work to be done before I can come to any publishable conclusion.