已知数列{an}(n∈N*)满足:an=logn+1(n+2)(n∈N*),定义使a1·a2·a3·……ak为整数的数k(k∈N*)叫做企盼

问题描述:

已知数列{an}(n∈N*)满足:an=logn+1(n+2)(n∈N*),定义使a1·a2·a3·……ak为整数的数k(k∈N*)叫做企盼
[1,2005]内所有企盼数的和M=

an=logn+1(n+2)=log2(n+2)/log2(n+1)
a1·a2·a3·……ak=log2(n+2)
n+2必须是2的n次幂才可以取的整数
M=(4-2)+(8-2)+(16-2)+…………+(1024-2)
=2^2+2^3+…………+2^10-2*9
=2026