Timeline for Bernoulli & Betti numbers (of manifolds) and the prime 34511

6 events

when toggle format	what		by	license	comment
Apr 1, 2021 at 13:46	comment	added	Timothy Chow		I don't know if this is how Carlo Beenakker did it, but one way to arrive at his identity is to search the OEIS for "34511 bernoulli"; this will take you to A096053. The OEIS will also tell you that 34511 divides $3^{17}-1$ (see A074477).
Apr 1, 2021 at 6:18	history	edited	Jens Reinhold	CC BY-SA 4.0	Added "even" somewhere where it is highly relevant
Mar 31, 2021 at 16:54	comment	added	Carlo Beenakker		$-\tfrac{1}{3}9^9 B_{18}(1/3)/B_{18}=1871\cdot 34511$
Mar 31, 2021 at 15:45	comment	added	Will Sawin		Similarly $p$ divides $2^{k-1}-1$ if and only if $k$ is congruent to $1$ modulo the order of $2$ mod $p$, which itself divides $p-1$. For $34511$ this is $595$. Thus once $k$ is a solution, anything congruent to $k$ mod $p-1$ is a solution.
Mar 31, 2021 at 15:35	comment	added	Will Sawin		The $p$-divisibility of the Bernoulli number $B_{2k}$ depends only on $2k \mod p-1$ (slightly simplified) so the reason $2^{23}$ shows up in one case and $2678$ shows up in the other should be because of the congruence $2^{23} \equiv 2678 \mod (34511-1)$.
Mar 31, 2021 at 15:16	history	asked	Jens Reinhold	CC BY-SA 4.0