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Let $n,a,b$ be positive integers with $a<b$. Consider primes of the form $f(n)=\dfrac{n^2-n+4}{2}$. Let $C(a,b)$ denote the amount of primes of the form $f(n)$ between (and including) $f(a)$ and $f(b) …

I posted a question on MSE about approximating Taylor series but Despite a bounty I did not receive any answers or comments. Maybe you guys can help. https://math.stackexchange.com/questions/1440931/p …

Let $n$ be a strict positive integer and let's define an integer sequence $f(n)$ : $$f(n) = \frac{n^2 + n + 4}{2}$$ so $$ \begin{split} f (\Bbb N)& \triangleq {3,5,8,12,17,23,30,38,47,\ldots}\\ f(1) …

Consider prime constellations $p,p+2s$ where both $p,p+2s$ are prime. For instance for $s=1$ we get the twin primes. We define the counting function $\pi_{2s}(n)$ to count the number of such pairs $p, …

Let $r(a,b)$ be a rational number depending on positive integers $a,b$ and $r(a,b)$ being nonnegative. For every $b$ there is an $a$ such that $r(a,b)$ is not $0$. Let $C(b)$ be a squarefree positive …