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...

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

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

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

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

finite sequences of symbols taken from a fixed alphabet) is called recursive if it is a recursive subset of the set of all possible finite sequences over...

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

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...

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

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)...

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...

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

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...

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...

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

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...

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...

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...

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

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

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

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

computable recursive formulas using Knuth's up-arrow notation or equivalent, as was done by Ronald Graham, the number's namesake. As there is a recursive formula...

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...

In particular, pairwise summation of a sequence of n numbers xn works by recursively breaking the sequence into two halves, summing each half, and adding...

mathematics a P-recursive equation is a linear equation of sequences where the coefficient sequences can be represented as polynomials. P-recursive equations...

be simply constants. A subset of these is the primitive recursive functions. Another example is the Ackermann function, which is recursively defined but...

sequences are then partitioned into r {\displaystyle r} parts and assigned to the appropriate processor groups. These steps are repeated recursively in...