the sequence $n!+2,...,n!+n$ is made up of only composite numbers
118383
If $n = 51! +1$, then find number of primes among $n+1,n+2,\ldots, n+50$
148901
Can a composite number $n$ be the arithmetic mean of $\sigma(n)$ and $\varphi(n)$?
12803
Proof for number of weak compositions
33177
All numbers of form $10^{k} + 1$ are composite for $k{\gt}2$ proof
109920
Ordered binary sequences of length n with no two consecutive 0's without using recursion
35515
Find the number of $(m+n)$ digit binary sequences with $m$ $0$'s and $n$ $1$'s such that no two $1$'s are adjacent
35553
If $n$ is composite, so is $2^n-1$
156660
The set of all strictly increasing sequences of natural numbers
35885
Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
22367
How do I prove that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite?
101766
Recursive sequence convergence.: $s_{n+1}=\frac{1}{2} (s_n+s_{n-1})$ for $n\geq 2$, where $s_1>s_2>0$
105882
Prove that the sequence with $T(0)=1$ and $T(n) = 1 + \sum_{j=0}^{n-1}T(j)$ is given by $T(n)=2^n$
54982
How to prove that $x_n=1+\frac{1}{2!}+\cdots+\frac{1}{n!}$ is a Cauchy sequence?
104268
Confusion on how to solve this question about sequences.
34588
Number Theory: $p!+p=n^2$, $p$ = prime
56624
Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers
114240
Need to prove the sequence $a_n=1+\frac{1}{2^2}+\frac{1}{3^2}+\cdots+\frac{1}{n^2}$ converges