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The sequence (α n) is equidistributed mod 1 for almost all values of α > 1. It is not known whether the sequences (e n ) or (π n ) are equidistributed mod 1. However it is known that the sequence (α n) is not equidistributed mod 1 if α is a PV number. Well-distributed sequence
In mathematics, the Erdős–Szekeres theorem asserts that, given r, s, any sequence of distinct real numbers with length at least ( r − 1) ( s − 1) + 1 contains a monotonically increasing subsequence of length r or a monotonically decreasing subsequence of length s. The proof appeared in the same 1935 paper that mentions the Happy Ending ...
SYN cookies. SYN cookie is a technique used to resist SYN flood attacks. The technique's primary inventor Daniel J. Bernstein defines SYN cookies as "particular choices of initial TCP sequence numbers by TCP servers." In particular, the use of SYN cookies allows a server to avoid dropping connections when the SYN queue fills up.
Interleave sequence. In mathematics, an interleave sequence is obtained by merging two sequences via an in shuffle . Let be a set, and let and , be two sequences in The interleave sequence is defined to be the sequence . Formally, it is the sequence given by.
The Internet Assigned Numbers Authority (IANA) maintains the official registry of HTTP status codes. All HTTP response status codes are separated into five classes or categories. The first digit of the status code defines the class of response, while the last two digits do not have any classifying or categorization role.
Pell number. In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins 1 1, 3 2, 7 5, 17 12, and 41 29, so the sequence of Pell numbers begins with 1, 2, 5, 12, and 29.
In a sociable sequence, each number is the sum of the proper divisors of the preceding number, i.e., the sum excludes the preceding number itself. For the sequence to be sociable, the sequence must be cyclic and return to its starting point. The period of the sequence, or order of the set of sociable numbers, is the number of numbers in this cycle.
Look-and-say sequence. The lines show the growth of the numbers of digits in the look-and-say sequences with starting points 23 (red), 1 (blue), 13 (violet), 312 (green). These lines (when represented in a logarithmic vertical scale) tend to straight lines whose slopes coincide with Conway's constant. In mathematics, the look-and-say sequence ...