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Let $a(n)$ be A300483. Here $$ a(n) = 2\int\limits_{t \geqslant 0}T_n\left(\frac{t+1}{2}\right)\exp(-t)\,dt. $$ where $T_n(x)$ is $n$-th Chebyshev polynomial of first kind. Let $b(n)$ be an integer ...

It is easy to see that every natural number $n$ can be written in a unique way $n = a+b$ where $gcd(a,b)=1$, $b>a$ and $b-a$ is minimal with this property. For instance if $n$ is odd the ...