Tootfinder

Integers with small digits in multiple bases
Thomas F. Bloom, Ernie Croot
https://arxiv.org/abs/2509.02835 https://arxiv.org/pdf/2509.02835

Integers with small digits in multiple bases
We show that, for any $r\geq 1$, if $g_1,\ldots,g_r$ are distinct coprime integers, sufficiently large depending only on $r$, then for any $ε>0$ there are infinitely many integers $n$ such that all but $ε\log n$ of the digits of $n$ are $\leq g_i/2$ in base $g_i$ for all $1\leq i\leq r$. In other words, for any fixed large bases, there are infinitely many $n$ such that almost all of the digits of $n$ are small in all bases simultaneously. This is both a quantitative and qualitative improvemen…

A BBP-type formula for the remainder of the Madhava-Gregory-Leibniz series
Benoit Cloitre
https://arxiv.org/abs/2507.20428 https://arxiv.org/pdf/2507.20428…

A BBP-type formula for the remainder of the Madhava-Gregory-Leibniz series
We derive a BBP-type formula for the remainder of the Madhava-Gregory-Leibniz series for $π$. The result is a closed form in base-$16$ with Pochhammer denominators. The analogous formula for the alternating series for $\log 2$ is also presented.