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You can do this in a single scan. Use a filestream and read one byte at a time. Just search for the first byte in teh sequence. When you find it, compare the rest of sequence to the contents of the file at that location. If not a match, continue.
Reading only one byte at a time is not efficient, but the filestream buffers the reads, I think. If it's still too slow, just modify the code to read and test 512 bytes at a time (which is good for NTFS) or 2048 at a time (which is good for CDs or FAT).