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Name First elements Short description OEIS Kolakoski sequence: 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, ... The n th term describes the length of the n th run : A000002: Euler's ...
Applying the f function k times to the number n = 2 k a + b will give the result 3 c a + d, where d is the result of applying the f function k times to b, and c is how many increases were encountered during that sequence. For example, for 2 5 a + 1 there are 3 increases as 1 iterates to 2, 1, 2, 1, and finally to 2 so the result is 3 3 a + 2 ...
The sequence 0, 3, 8, 15, ... is formed according to the formula n 2 − 1 for the nth 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.
In mathematics, a sequence of natural numbers is called a complete sequence if every positive integer can be expressed as a sum of values in the sequence, using each value at most once. For example, the sequence of powers of two (1, 2, 4, 8, ...), the basis of the binary numeral system, is a complete sequence; given any natural number, we can ...
The On-Line Encyclopedia of Integer Sequences ( OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching at AT&T Labs. He transferred the intellectual property and hosting of the OEIS to the OEIS Foundation in 2009. [4] Sloane is the chairman of the OEIS Foundation.
In mathematics, 1 + 2 + 4 + 8 + ⋯ is the infinite series whose terms are the successive powers of two. As a geometric series, it is characterized by its first term, 1, and its common ratio, 2. As a series of real numbers it diverges to infinity, so the sum of this series is infinity. However, it can be manipulated to yield a number of ...
The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...
1 − 2 + 4 − 8 + ⋯. In mathematics, 1 − 2 + 4 − 8 + ⋯ is the infinite series whose terms are the successive powers of two with alternating signs. As a geometric series, it is characterized by its first term, 1, and its common ratio, −2. As a series of real numbers, it diverges. So in the usual sense it has no sum.