The Simpsons opening sequence chalkboard and couch gags filmed. Attached to the end of this sequence is the message "Come home to "The Simpsons" on Sky One." The recreation was used instead of the regular opening titles in the season 17 episode "Homer Simpson, This Is Your Wife", first broadcast on the Fox network on March 26, 2006. The live-action opening had also become an Internet hit before it was aired in front of "Homer Simpson, This Is Your Wife", and it was Groening's decision to use it. Al Jean commented in a press statement that he was "just amazed there are people who
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