def f2(n)
	return n.odd? ? (n * 3 + 1) / 2 : n / 2

end

def re(n, t)

	s = (n % 2).to_s
	n1 = n
	t.times \
	{
		n = f2(n)
		s << (n % 2).to_s
	}
	return s
end


p = (1..20).map { rand(2) }.join

p2 = p[0, 1]
(1...p.length).each \
{
	|x|
	n = p2.reverse.to_i(2)
	s = re(n, x)
	b = s[-1, 1]
	p2 += (b == p[x, 1]) ? '0' : '1'
	p([s, n, n.to_s(2).reverse])
}

n = p2.reverse.to_i(2)
s = re(n, p.length - 1)
p([s, n, n.to_s(2).reverse, p == s])