Warren Beatty if its regular host comedians, Milton Berle. Beatty learned to do a "superb imitation of Berle and his routine," said a friend, and he often used Berle-type humor at home. His sister Shirley MacLaine's lasting memories of her brother include seeing him reading books by Eugene O'Neill or singing along to Al Jolson records. In "Rules Don't Apply" (2016), Beatty plays Howard Hughes, who is shown talking about and singing Jolson songs while flying his plane. MacLaine noted, on what made her brother want to become a filmmaker, sometimes writing, producing, directing and starring in his films: "That's why he's
Beatty sequence then formula_4 is also a positive irrational number. These two numbers naturally satisfy the equation formula_5. The two Beatty sequences they generate, form a "pair of complementary Beatty sequences". Here, "complementary" means that every positive integer belongs to exactly one of these two sequences. For "r" = the golden mean, we have "s" = "r" + 1. In this case, the sequence formula_8, known as the "lower Wythoff sequence", is and the complementary sequence formula_9, the "upper Wythoff sequence", is These sequences define the optimal strategy for Wythoff's game, and are used in the definition of the Wythoff array As