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In mathematics, the Skolem problem is the problem of determining whether the values of a constant-recursive sequence include the number zero. The problem can be formulated for recurrences over different types of numbers, including integers, rational numbers, and algebraic numbers.
In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.
The most-common visualization of the Recamán's sequence is simply plotting its values, such as the figure seen here. On January 14, 2018, the Numberphile YouTube channel published a video titled The Slightly Spooky Recamán Sequence , [ 3 ] showing a visualization using alternating semi-circles, as it is shown in the figure at top of this page.
The function can be extended to sequences of actions by the following recursive equations: (, [ ]) = (, [,, …,]) = ( (,), [, …,]) A plan for a STRIPS instance is a sequence of actions such that the state that results from executing the actions in order from the initial state satisfies the goal conditions.
The Fibonacci sequence is constant-recursive: each element of the sequence is the sum of the previous two. Hasse diagram of some subclasses of constant-recursive sequences, ordered by inclusion In mathematics , an infinite sequence of numbers s 0 , s 1 , s 2 , s 3 , … {\displaystyle s_{0},s_{1},s_{2},s_{3},\ldots } is called constant ...
Recursive drawing of a Sierpiński Triangle through turtle graphics. In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. [1] [2] Recursion solves such recursive problems by using functions that call themselves from within their own code ...
The ordinary generating function of a sequence can be expressed as a rational function (the ratio of two finite-degree polynomials) if and only if the sequence is a linear recursive sequence with constant coefficients; this generalizes the examples above. Conversely, every sequence generated by a fraction of polynomials satisfies a linear ...
where append(n,s,x) computes, whenever s encodes a sequence of length n, a new sequence t of length n + 1 such that t[n] = x and t[i] = s[i] for all i < n. This is a primitive recursive function, under the assumption of an appropriate Gödel numbering; h is assumed primitive recursive to begin with. Thus the recursion relation can be written as ...