Question

已知函数f(n)=log(n+1)(n+2)(n∈N*),定义使f(1),f(2)……f(K)为整数的数k(k∈N*)叫

Answer 1

1＜f(n)=log(n+1)(n+2)≤100

n+1＜(n+1)^f(n)=n+2≤(n+1)^100

n≥1

3＜2^f1≤n+2≤(n+1)^100,

f1≥2

4≤2^f1≤n+2≤(n+1)^100,

n≥2

4≤3^f2≤n+2≤(n+1)^100

f2≥2,

9≤3^f2≤n+2≤(n+1)^100

n≥7

9≤8^f7≤n+2≤(n+1)^100

f7≥2,

64≤8^f7≤n+2≤(n+1)^100

n≥62

64≤63^f62≤n+2≤(n+1)^100

f62≥2,

63^2≤63^f62≤n+2≤(n+1)^100

所以填0.