Convergent series of integers with missing digits

On Binary Representations of Integers with Digits

Güntzer and Paul introduced a number system with base 2 and digits −1, 0, 1 which is characterized by separating nonzero digits by at least one zero. We find an explicit formula that produces the digits of the expansion of an integer n which leads us to many generalized situations. Syntactical properties of such representations are also discussed. 1. A binary number system Integers n can be wri...

Approximate Polynomial GCD over Integers with Digits-wise Lattice

For the given coprime polynomials over integers, we change their coefficients slightly over integers so that they have a greatest common divisor (GCD) over integers. That is an approximate polynomial GCD over integers. There are only two algorithms known for this problem. One is based on an algorithm for approximate integer GCDs. The other is based on the well-known subresultant mapping and the...

On Cantor's Series with Convergent

On the Sum of Digits of Some Sequences of Integers

Let b ≥ 2 be a fixed positive integer. We show for a wide variety of sequences {an}n=1 that for most n the sum of the digits of an in base b is at least cb log n, where cb is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.

A Class of Convergent Series with Golden Ratio Based on Fibonacci Sequence

In this article, a class of convergent series based on Fibonacci sequence is introduced for which there is a golden ratio (i.e. $frac{1+sqrt 5}{2}),$ with respect to convergence analysis. A class of sequences are at first built using two consecutive numbers of Fibonacci sequence and, therefore,  new sequences have been used in order  to introduce a  new class of series. All properties of the se...