Yes, I know it sounds odd. Sequential and Binary-splits don't mix.. That is unless the sequence is the byte offset within the file itself...
I've scrambled together a binary split search in bash script, using dd. It has Search-and-Find times of 3-9 seconds for an 8 GB file.. so it works (but slower than I know it can be)... I'd really prefer to not have to polish this wheel; It just took my fancy to do it as an exercise in bash (having a project is the best way to learn a language, etc). I think this would be pretty straight forward in C/++, etc... I'm curious to see some other examples (particularly bash ones.