No remainder

Let F(n)=11+105^n Let S be the serie of F(n) values for n=1,2,...: 116, 11036, 1157636, 121550636, 12762815636, 1340095640636, ... What is the 10^4-th term that can be divided by 27126986671934931497 with no remainder. Answer format: the term mod 10^9 [My timing: 3s]