Homer Simpson, This Is Your Wife The large number of viewers of "Homer Simpson, This Is Your Wife" was the result of Gervais' involvement—new episodes of the show were usually seen by approximately one million people on Sky1 at the time. Instead of the usual animated opening sequence that is played in front of "The Simpsons" episodes, this episode began with a live-action opening sequence. The sequence, which mirrors the normal opening but with real-life actors and locations, was originally created by British Sky Broadcasting for Sky1's promotion of "The Simpsons". The live-action opening had already become an Internet hit before it was aired in front
Automatic sequence is a fixed point of φ—that is, if "w" = φ("w")—then "s" = τ("w") is a "k"-automatic sequence. This result is due to Cobham, and it is referred to in the literature as "Cobham's theorem". Conversely, every "k"-automatic sequence is obtainable in this way. Let "k" ≥ 2. The "k-kernel" of the sequence "s"("n") is the set of subsequences In most cases, the "k"-kernel of a sequence is infinite. However, if the "k"-kernel is finite, then the sequence "s"("n") is "k"-automatic. It follows that a "k"-automatic sequence is necessarily a sequence on a finite alphabet. Let "u"("n") be a sequence