# Tagged Questions

15 views

### Sequence terms being divisible

Here's a question I would like hints for: The sequence ${x_n}$ is defined by $x_{n+2}=6x_{n+1}-9x_{n}$ for $n \geq 0$ where $x_0=3$ and $x_1=18$. What is the smallest $k$ such that $x_k$ is ...
20 views

### Unique sum between elements of a numerical set

I require a set of numerical elements on wich the sum of some of these elements is unique to the set, that it's to say, no other combination in the sum of elements will result the same outcome. ...
25 views

### Given a positive integer $k$, find the integer part of $n^2 /k$ for $n\ge 1$, and a related question.

For a given positive integer $k,$ I am looking for possible answers / literature about the sequence $(a_n)=([\frac{n^2}{k}])_{n=1}^\infty$, where $[x]=$the integer part of $x.$ This question is ...
43 views

49 views

### A general question on positive integer sequence of a certain formula

Let $A=\{\$ a certain polynomial | all variables$\ \in\mathbb N\ \},\ A\ \subseteq\ \mathbb Z^+,\$ such as $A = \{2n−1\ |\ n\in\mathbb N\}$. Let $B=\mathbb Z_{\ge 0}-A$. Let $C$ be the set that ...
81 views

### Combining primes for getting primes?

I was thinking about what would happen when we combine two prime numbers $p$ and $q$ into one number $:pq:$ . Like if $p=5$ and $q=3$ , then $:pq:=53$ . Then if $p=7$ and $q= 11$ then $:pq:=711$ and ...
### Question about the convergence of an infinite series in all of $\mathbb{C}$.
Does the following infinite series: $$G(s):=\displaystyle \sum^{\infty}_{n=1} \frac{(-1)^{n+1}}{n^s + \frac{1}{n^s}}$$ converge for all $s \in \mathbb{C}$ (especially in the critical strip; since ...