The Simpsons opening sequence hoisting Martin Prince up a flagpole by his underwear and saluting it as if it were a flag. The camera then zooms through a window of the school where Bart is doing the chalkboard gag which is "I will not illegally download this movie", a reference to piracy before quick-fading to the popular 90s band Green Day who are hosting a concert at Lake Springfield, playing their rendition of "The Simpsons Theme". "He Loves to Fly and He D'ohs" (season 19) was the first new episode to air following the release of "The Simpsons Movie", and the episode's opening sequence
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