The Mary Tyler Moore Show opening sequence opening sequence, with Alexei Sayle dancing through the streets of London to the theme song 'Life's a Big Banana Sandwich'. In the "Saturdays of Thunder" episode of "The Simpsons" (also produced by "Mary Tyler Moore" creator James L. Brooks), Homer criticizes his sister-in-law Patty's Mary Tyler Moore style hairdo, to which her sister Selma insists he be ignored, retorting, "You can turn the world on with your smile," in reference to the theme song's opening lyric. A 1984 episode of "Saturday Night Live" included a sketch that quoted the theme. Guest-host Ed Asner (who had played Lou Grant on "Mary
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