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Katydid Sequence
The Katydid sequence is a sequence of numbers first defined in Clifford A. Pickover Clifford Alan Pickover (born August 15, 1957) is an American author, editor, and columnist in the fields of science, mathematics, science fiction, innovation, and creativity. For many years, he was employed at the IBM Thomas J. Watson Research ...'s book ''Wonders of Numbers'' (2001). Description A Katydid sequence is the smallest sequence of integers that can be reached from 1 by a sequence of the two operations ''n'' ↦ 2''n'' + 2 and 7''n'' + 7 (in any order). For instance, applying the first operation to 1 produces the number 4, and applying the second operation to 4 produces the number 35, both of which are in the sequence. The first 10 elements of the sequence are: :1, 4, 10, 14, 22, 30, 35, 46, 62, 72. Repetitions Pickover asked whether there exist numbers that can be reached by more than one sequence of operations. The answer is yes. For instance, 1814 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Sequence
In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified ''explicitly'' by giving a formula for its ''n''th term, or ''implicitly'' by giving a relationship between its terms. For example, the sequence 0, 1, 1, 2, 3, 5, 8, 13, ... (the Fibonacci sequence) is formed by starting with 0 and 1 and then adding any two consecutive terms to obtain the next one: an implicit description. The sequence 0, 3, 8, 15, ... is formed according to the formula ''n''2 − 1 for the ''n''th term: an explicit definition. Alternatively, an integer sequence may be defined by a property which members of the sequence possess and other integers do not possess. For example, we can determine whether a given integer is a perfect number, even though we do not have a formula for the ''n''th perfect number. Examples Integer sequences that have their own name include: *Abundant numbers *Baum–Sweet sequence *Bell numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford A
Clifford may refer to: People *Clifford (name), an English given name and surname, includes a list of people with that name * William Kingdon Clifford *Baron Clifford * Baron Clifford of Chudleigh *Baron de Clifford * Clifford baronets *Clifford family (bankers) *Jaryd Clifford *Justice Clifford (other) *Lord Clifford (other) Arts, entertainment, and media *''Clifford the Big Red Dog'', a series of children's books **Clifford (character), the central character of ''Clifford the Big Red Dog'' ** ''Clifford the Big Red Dog'' (2000 TV series), 2000 animated TV series **''Clifford's Puppy Days'', 2003 animated TV series **''Clifford's Really Big Movie'', 2004 animated movie ** ''Clifford the Big Red Dog'' (2019 TV series), 2019 animated TV series ** ''Clifford the Big Red Dog'' (film), 2021 live-action movie * ''Clifford'' (film), a 1994 film directed by Paul Flaherty *Clifford (Muppet) Mathematics *Clifford algebra, a type of associative algebra, named after William ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
