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 if it satisfies...

sequence Ulam numbers Weird numbers Wolstenholme number Constant-recursive sequence On-Line Encyclopedia of Integer Sequences List of OEIS sequences Hamkins...

problem in mathematics Is there an algorithm to test whether a constant-recursive sequence has a zero? More unsolved problems in mathematics In mathematics...

"Linear recursive sequences". SIAM Rev. Vol. 10, no. 3. pp. 324–353. JSTOR 2027658. Brousseau, Alfred (1971). Linear Recursion and Fibonacci Sequences. Fibonacci...

sequence Thue–Morse sequence List of integer sequences Types ±1-sequence Arithmetic progression Automatic sequence Cauchy sequence Constant-recursive...

with Euler's constant, a different constant typically denoted γ {\displaystyle \gamma } . Alternatively, e can be called Napier's constant after John Napier...

base) in some recursive order. For instance, the binary Champernowne sequence in shortlex order is 0 1 00 01 10 11 000 001 ... (sequence A076478 in the...

study of recursive functions, ones which repeat previous values and generate sequences based on these values. Kaprekar's routine is a recursive arithmetic...

One's parent (base case), or One's parent's ancestor (recursive step). The Fibonacci sequence is another classic example of recursion: Fib(0) = 0 as...

In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all...

Lucas sequences U n ( P , Q ) {\displaystyle U_{n}(P,Q)} and V n ( P , Q ) {\displaystyle V_{n}(P,Q)} are certain constant-recursive integer sequences that...

combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients: ch. 17 : ch. 10  (also known as a linear recurrence relation...

the sequence of its coefficients, in one or several indices, is also called holonomic. Holonomic sequences are also called P-recursive sequences: they...

binary sequence representing the real number is an algorithmically random sequence. Calude, Hertling, Khoussainov, and Wang showed that a recursively enumerable...

clockwise. It suffices to represent the sequence of disks to be moved. The solution can be found using two mutually recursive procedures: To move n disks counterclockwise...

In mathematics, the Fibonacci numbers form a sequence defined recursively by: F n = { 0 n = 0 1 n = 1 F n − 1 + F n − 2 n > 1 {\displaystyle...

In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of N {\displaystyle N} , its subsequence x 1 , … , x N {\displaystyle...

solutions to smaller instances of the same problem. Recursion solves such recursive problems by using functions that call themselves from within their own...

other scales. Bertran Steinsky has created a recursive formula for the i-th term of the sequence. The sequence is not eventually periodic, that is, its terms...

nonnegative integer appear in Recamán's sequence? Skolem problem: can an algorithm determine if a constant-recursive sequence contains a zero? The values of g(k)...

pages follow describing how such sequences might be contrived in general. The m-th term of any constant-recursive sequence (such as Fibonacci numbers or...

MR 0163867 Pethő, Attila (2001), "Diophantine properties of linear recursive sequences II", Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, 17:...

ISBN 978-3-540-44141-0. Zbl 1014.11015. Richman, Robert (2001). "Recursive Binary Sequences of Differences" (PDF). Complex Systems. 13 (4): 381–392. Bugeaud...

recursive detail at increasing magnifications; mathematically, the boundary of the Mandelbrot set is a fractal curve. The "style" of this recursive detail...

In mathematics, the Perrin numbers are a doubly infinite constant-recursive integer sequence with characteristic equation x3 = x + 1. The Perrin numbers...

background (Figure-Figure sequence) and chapter V on recursive structures and processes (remaining sequences), these sequences are: The Hofstadter Figure-Figure...

where c i {\displaystyle c_{i}} are complex number constants (i.e., a constant-recursive sequence of order d {\displaystyle d} ). Then the set of zeros...

limit of a uniformly computable sequence of functions. The terms computable in the limit, limit recursive and recursively approximable are also used. One...

function In each recursive call, the least significant digits of the binary representation of n is removed. It follows that the number of recursive calls is ⌈...

new sub-problems. For example, consider the recursive formulation for generating the Fibonacci sequence: Fi = Fi−1 + Fi−2, with base case F1 = F2 = 1...