grow7.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 mx(n)
	return {'ls' => seq2(n).size}
	
end

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

def stat(l)
        return if (l.empty?)
        t = t2 = 0
        l.each \
        {
		|x|
		t += x
		t2 += x ** 2
        }
        c = l.size
        a = t.to_f / c
        z = t2.to_f / c - a ** 2
        sd = Math.sqrt(z < 0 ? 0 : z)

	return l.size, a, sd, l.max, l.min
end


l = [{'n' => 1, 'p' =>0}.merge(mx(1))]

a = {}
t1 = Time.now.to_i

loop \
{
	l = l.sort_by { |x| -x['ls'] }
	
	x = l.delete_at(rand([l.size, 50].min))

	p = x['p'] + 1
	n = x['n']
	
	x1 = x.dup
	x1['p'] = p
	l.push(x1)
	
	x2 = {}
	n |= (1 << p)
	
	x2['n'] = n
	x2['p'] = p
	x2.merge!(mx(n))
	if (x2['ls'] > x['ls']) then
		l.push(x2) 
#		j = p
		j = x2['ls']
		a[p] = a.fetch(p, []) + [x2]
		t = sprintf("%.1fm\n", (Time.now.to_i - t1).to_f / 60).to_f
		$stderr.puts([l.size, t].inspect) if (l.size % 100 == 0)
	end
	break if (l.size == 2000)
}

a.keys.sort.each \
{
	|i|
	l = a[i].map { |x| d(x['n'].to_s(2)) }
	puts(([i] + stat(l)).join("\t"))
}