hard.rb

def f1(n)
        n = (n * 3 + 1) / 2 while (n % 2 == 1)
        n /= 2 while (n % 2 == 0)
        return n
end

def seq2(n)
	l = [n]
	n1 = n
		
	l << (n = f1(n)) while (n >= n1 && n != 1)
	return l
end

def d(s)
        c = s.split('').select { |x| x == '1' }.size
	d = c.to_f / s.length
        return d
        
end

def val(z)
	n = z['n']
	l = seq2(n)

	cm = (0...l.size).max_by { |x| l[x] }
	ns = n.to_s(2)
	d = d(ns)
	nl = ns.length
	return z.merge({'cm' => cm, 'nl' => nl, 'd' => d, 'by' => nl - cm})
end

def hard(c)
		
		
	l = [val({'n' => 1, 'p' =>0})]
	
	c.times \
	{
		l.sort_by! { |x| [x['by'], x['d']] }

		x = l.delete_at(rand([l.size, 100].min))
		
		
		p = x['p'] + 1
		
		l.push(x.merge('p' => p))
		l.push(val({'n' => x['n'] | (1 << p), 'p' => p}))
		
		$stderr.puts([l.size, x].inspect)
	}
	return l
	
end

l = hard(5000)

l[0...10].each { |x| $stderr.puts(x.inspect) }

$stderr.puts(l[0].keys.inspect)
l.sort_by! { |x| x['n'] }.each { |x| p(x.values) }