mick
Consider
$$ y = \int_1^{\infty} \frac{\operatorname{li}(x)^2 (x - 1)}{x^4} dx, $$
where $\operatorname{li}(x)$ is the logarithmic integral. Is there a closed form for y ?
It appears that a good approximation is $ 10 \cdot \operatorname{Ci}\bigl( \frac{56}{19}\bigr)$, where $\operatorname{Ci}(x)$ ...
Consider
$$A = 1+\dfrac{2+\dfrac{3+\dfrac{4+\cdots}{5+\cdots}}{4+\dfrac{5+\cdots}{6+\cdots}}} {3+\dfrac{4+\dfrac{5+\cdots}{6+\cdots}}{5+\dfrac{6+\cdots}{7+\cdots}}} $$
and
$$B = 1+\dfrac{3+\dfrac{5+\dfrac{7+\cdots}{6+\cdots}}{4+\dfrac{6+\cdots}{5+\cdots}}} {2+\dfrac{4+\dfrac{6+\cdots}{5+\cdots}}{...
I was thinking about knight tours.
https://en.wikipedia.org/wiki/Knight%27s_tour
I also wonder about knight tours for bigger boards such as 10x10 or 12x12.
Maybe this belong more in a puzzle group or math group, but I take my chances here.
Migration is an option as I am also active on mathstack.
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