[seqfan] Re: A324370 and A318256 related to Bernoulli fractions

[Peter Luschny]

 jean-paul allouche:

Is it not essentially in the paper of Bernd C. Kellner and Jonathan Sondow,
> Power-Sum Denominators, Amer. Math. Monthly, 124 (2017), 695-709,
> doi:10.4169/amer.math.monthly.124.8.695, arXiv:1705.03857
> (referred to in the OEIS about these two sequences)?
>

Yes, sure. As Kellner and Sondow explain in the Monthly this
sequence has two representations, one using Bernoulli
polynomials and a second one without Bernoulli, using
base p representations etc. Well documented in the OEIS, see
for example in A195441, May 14 2017 or in A144845, May 15 2017.
No need here to check anything numerically.

We have the following identities, for n >= 0:
A324370(n+1) = A195441(n)/A324369(n+1)
                        = A144845(n)/A007947(n+1) = A318256(n).

The two sequences have a different offset though. One might
regret that. On the other hand it feels natural to start the
Bernoulli based sequence with n=0 and the other with n=1.
I think it is OK to leave things as they are.

What I do not like is the way the sequence was approved. It
would have been the editor's job to discuss in the review with
the authors if a second sequence really is necessary. But the
approving editor apparently prefers quick and lonely decisions,
based on the reputation of authors more than a professional
discussion. At least he should have insisted on a cross-reference,
but more importantly give other editors the chance to understand
the decision of Kellner and Sondow to duplicate the sequence.