A number n is called a double if its base-7 digits form the base-10 number 2n. For example, 51 is 102 in base 7. What is the largest double?

Prove that in any acute triangle of sides a,b,c semiperimeter p ,inradius r and circumradius R, the following inequalities hold : 2/5 < Rp/(2aR+bc) < 1/2.