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The process of generating a Kasami sequence is initiated by generating a maximum length sequence a(n), where n = 1…2 N −1. Maximum length sequences are periodic sequences with a period of exactly 2 N −1. Next, a secondary sequence is derived from the initial sequence via cyclic decimation sampling as b(n) = a(q ⋅ n), where q = 2 N/2 +1.
Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})
Recamán's sequence: 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ... "subtract if possible, otherwise add": a(0) = 0; for n > 0, a(n) = a(n − 1) − n if that number is positive and not already in the sequence, otherwise a(n) = a(n − 1) + n, whether or not that number is already in the sequence. A005132: Look-and ...
It supports macOS including Apple Silicon-based. It's a free compiler, though it also has commercial add-ons (e.g. for hiding source code). Numba is used from Python, as a tool (enabled by adding a decorator to relevant Python code), a JIT compiler that translates a subset of Python and NumPy code into fast machine code.
For example, a Ducci sequence starting with the n-tuple (1, q, q 2, q 3) where q is the (irrational) positive root of the cubic = does not reach (0,0,0,0) in a finite number of steps, although in the limit it converges to (0,0,0,0).
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, (sequence A000396 in the OEIS), even though we do not have a formula for the nth perfect number.
A Fibonacci sequence of order n is an integer sequence in which each sequence element is the sum of the previous elements (with the exception of the first elements in the sequence). The usual Fibonacci numbers are a Fibonacci sequence of order 2.
In mathematics and computer science, Recamán's sequence [1] [2] is a well known sequence defined by a recurrence relation. Because its elements are related to the previous elements in a straightforward way, they are often defined using recursion .