Related papers: Approximations of generating functions and a few c…
Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…
In the following pages we discuss infinite sequences defined on a finite alphabet, and more specially those which are generated by finite automata. We have divided our paper into seven parts which are more or less self-contained. Needless…
Operators on probability distributions can be expressed as operators on the associated moment sequences, and so correspond to operators on integer sequences. Thus, there is an opportunity to apply each theory to the other. Moreover,…
The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
The determination of block-entropies is a well established method for the investigation of discrete data, also called symbols (7). There is a large variety of such symbolic sequences, ranging from texts written in natural languages,…
In a paper entitled Binary lambda calculus and combinatory logic, John Tromp presents a simple way of encoding lambda calculus terms as binary sequences. In what follows, we study the numbers of binary strings of a given size that represent…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
Provably correct software is one of the key challenges in our softwaredriven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction.…
A case is made that researchers are interested in studying processes. Often the inferences they are interested in making are about the process and its associated population. On other occasions, a researcher may be interested in making an…
A decomposition of a natural number n is a sequence of consecutive natural numbers that sums to n. We construct a one-to-one correspondence between the odd factors of a natural number and its decompositions. We study the decompositions by…
In this article, we give a particular recreational application of the sequence A000533 and A261544 in "The On-line Encyclopedia of Integer Sequences" (OEIS). The recreational application provides a direct extension to "The Repetitious…
We present a benchmark of 29687 problems derived from the On-Line Encyclopedia of Integer Sequences (OEIS). Each problem expresses the equivalence of two syntactically different programs generating the same OEIS sequence. Such programs were…
We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented.
We introduce a new permutation statistic, namely, the number of cycles of length $q$ consisting of consecutive integers, and consider the distribution of this statistic among the permutations of $\{1,2,...,n\}$. We determine explicit…
Stochastic computing (SC) is a high density, low-power computation technique which encodes values as unary bitstreams instead of binary-encoded (BE) values. Practical SC implementations require deterministic or pseudo-random number…
A Lambert series generating function is a special series summed over an arithmetic function $f$ defined by \[ L_f(q) := \sum_{n \geq 1} \frac{f(n) q^n}{1-q^n} = \sum_{m \geq 1} (f \ast 1)(m) q^m. \] Because of the way the left-hand-side…
This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…
A probabilistic program defines a probability measure over its semantic structures. One common goal of probabilistic programming languages (PPLs) is to compute posterior probabilities for arbitrary models and queries, given observed…
In this paper, we give recurrence relations and identities for some integer sequences related to Ward numbers such as Ward-Lah numbers, varied Ward numbers and binomial Ward numbers. Most of the sequences are entered in the On-Line…