# Tagged Questions

Use this tag if your question is about a well-known conjecture or a conjecture of your own.

231 views

### I conjecture that there are infinitely many linear relations $p_n + p_{n + 3} = 2 p_{n + 2}$ in the sequence of primes!

Let $p_1 < p_2 < p_3 < \ldots < p_n < \ldots$ be the sequence of primes (with $p_1 := 2$ as usual). Conjecture: There are infinitely many positive integers $n$ for which \begin{...
161 views

99 views

167 views

### a conjectured new generating function of narayana's sequence

In the 14th century ,an Indian mathematician T.V Narayana came up with a sequence now named after him.The sequence satisfies the recurrence $$a_{n}=a_{n-1}+a_{n-3}$$ Starting with $a_{0}=a_{1}=1$, ...
197 views

152 views

### conjecture about primes and a certain q-series.

Using wolfram Mathematica ,I observed an interesting and surprising property concerning prime numbers and q-series which I could not prove.Yet there is strong evidence supporting it. I would be happy ...
103 views

### Can the sum of 3 unique primes be expressed as the sum of 2 primes?

Let's consider the example, $$3 + 11 + 19 = 33 \\ 2 + 31 = 33$$ we can see that there are cases where the sum of 3 primes be expressed as the sum of 2 primes. However, I couldn't find a case ...
75 views

### If $(a_n)$ is increasing and $a_n^{1/c^n}\to\infty$, then $\sum\frac1{a_n}$ is irrational?

I $\DeclareMathOperator\lcm{lcm}$am trying to generalise the result from this question: If $(a_n)$ is increasing and $\lim_{n \to \infty} a_n^{1/2^n} = \infty$, show that $\sum_{k=1}^{\infty} 1/{a_n}$ ...
69 views

### Improved Betrand's postulate

I want to show that $2p_{n-2} \geq p_{n}-1$... Bertand's postulate shows us that $4p_{n-2}\geq p_{n}$ but can we improve on this? any ideas?
56 views

### Sum involving the number of zeros of $k$

I'm currently interested in sums involving digit-functions. Especially, I'd like to calculate the following sum: $$s=\sum_{k=1}^{\infty}{\frac{a_0(k)}{k\left(k+1\right)}}$$ Where $a_0(k)$ is the ...
168 views

222 views

### Does the set of $m \in Max(ord_n(k))$ for every $n$ without primitive roots contain a pair of primes $p_1+p_2=n$?

I have made the following observation: for those n even numbers that do not have primitive roots modulo n ,$Pr(n)$, the set $M(n)$ of those $k$ having a maximum multiplicative order $ord_n(k)$ ...
79 views

### Conjecture: only one even Fibonacci term divided by two gives a prime: $F(9) = 34 = 2 \times 17$

Every Fibonacci term $F(3n)$ is divisible by two $F(3) = 2$ $F(6) = 8$ $F(9) = 34$ $...$ After seeking Fibonacci tables factorization until $F(10000)$, for every term $\frac{F(3n)}{2}$, it ...
162 views

### Conjecture about the product of the primitive roots modulo a prime number ($\prod Pr_p$)

While I was learning about the primitive roots modulo $p \in \Bbb P$ (I will call $Pr_p$ to the complete list of the primitive roots module $p$) and having in mind the conjecture explained in this ...