Related papers: Classes of Gap Balancing Numbers
There is a growing literature on sums of reciprocals of polynomial functions of recurrence relations with constant coefficients and fixed depth, such as Fibonacci and Tribonacci numbers, products of such numbers, and balancing numbers…
Repdigits are natural numbers formed by the repetition of a single digit. In this paper, we study the problem of writing repdigits as the difference of two balancing or Lucas-balancing numbers. The method of proof involves the application…
The well known Three Gap Theorem states that there are at most three gap sizes in the sequence of fractional parts $\{\alpha n\}_{n<N}$ . It is known that if one averages over {\alpha}, the distribution becomes continuous. We present an…
Repdigits are natural numbers formed by the repetition of a single digit. In this paper, we explore the presence of repdigits in the product of consecutive balancing or Lucas-balancing numbers.
In this paper, we define Gaussian generalized Tetranacci numbers and as special cases, we investigate Gaussian Tetranacci and Gaussian Tetranacci-Lucas numbers with their properties.
We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and always having the next term be either the sum or the difference…
We study the gaps between consecutive prime numbers directly through Eratosthenes sieve. Using elementary methods, we identify a recursive relation for these gaps and for specific sequences of consecutive gaps, known as constellations.…
In multi-task learning (MTL), gradient balancing has recently attracted more research interest than loss balancing since it often leads to better performance. However, loss balancing is much more efficient than gradient balancing, and thus…
We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…
We define recursive harmonic numbers as a generalization of harmonic numbers. The table of recursive harmonic numbers, which is like Pascal's triangle, is constructed. A formula for recursive harmonic numbers containing binomial…
We study the difference between the number of facets of the order polytope and the chain polytope of a poset. Hibi and Li classified posets where the gap is exactly zero. We describe the bounds on this gap using the new notion of crossing…
An overview of the results of new exhaustive computations of gaps between primes in arithmetic progressions is presented. We also give new numerical results for exceptionally large least primes in arithmetic progressions.
For a natural number $N\geq 2$ and a real $\alpha$ such that $0 < \alpha \leq \sqrt{N}-1$, we define $I_\alpha:=[\alpha,\alpha+1]$ and $I_\alpha^-:=[\alpha,\alpha+1)$ and investigate the continued fraction map $T_\alpha:I_\alpha \to…
We define interval spacing as the difference in the order statistics of data over a gap of some width. We derive its density, expected value, and variance for uniform, exponential, and logistic variates. We show that interval spacing is…
A lifting of a semilattice S is an algebra A such that the semilattice of compact (=finitely generated) congruences of A is isomorphic to S. The aim of this work is to give a categorical theory of partial algebras endowed with a partial…
The article focuses on the problems of prime gaps and zero spacings. Possible solutions of several related problems such as the greatest lower bound, the least upper bound of the zero spacings, and the least upper bound of the prime gaps…
Consider a plane graph G, drawn with straight lines. For every pair a,b of vertices of G, we compare the shortest-path distance between a and b in G (with Euclidean edge lengths) to their actual distance in the plane. The worst-case ratio…
In present work, we find a class of Lie algebras, which are defined from the symmetrizable generalized intersection matrices. However, such algebras are different from generalized intersection matrix algebras and intersection matrix…
In this article, a relation between a gap $d_{k}$ and divisors of composite numbers between $p_{k}$ and $p_{k+1}$ is established.
The article contains some important classes of multisets. Combinatorial proofs of problems on the number of m-submultisets and m-permutations of multiset elements are considered and effective algorithms for their calculation are given. In…