I am so sorry for misleading you. I needed to solve this problem, because it occurred to me whilst I was solving another one. Indeed, what I had written is not true. In such case, could you help me find all integers for which
You could try to show that the ratio increases towards a limiting value 4. The ratio is equal to 3 when n=1. For n>1, it will lie between 3 and 4, so can never again be an integer.