# [seqfan] Re: Comment on A151750 [erratum]

peter.luschny peter.luschny at googlemail.com
Sun Aug 2 21:34:02 CEST 2009

```DW> Please restate the problem.

The proposition ...

The case p does not divide choose(2n, n) <=>
n has all base-p digits < p/2.

... has a nice generalization in terms of the swinging
factorial. In the setup of the swinging factorial
choose(2n, n) is just the even cases. Why cast away
half of the result?

However, I was not concerned with this in my original
posting at all. I just answered to what you wrote.

The subject points to A151750, which in turn points
to A030979, A129508.

A151750 Numbers n such that GCD(binomial(2n,n), 3*5*7*11) = 1.
A030979 Numbers n such that C(2n,n) is not divisible by 3, 5 or 7.
A129508 Numbers n such that 3 and 5 do not divide binomial(2n,n).

After reading these three titles I considered whether these
cases can be formulated uniformly in a more general frame.

See my original posting where I tried to explain what my
thoughts were. It let me to the sequence 6,20,1512,6320,...
where 6320 is twice the 3160 from A151750.

--------------------------------------------------

Please restate the problem.

----- Original Message -----
From: "peter.luschny" <peter.luschny at googlemail.com>
To: <seqfan at list.seqfan.eu>
Sent: Sunday, August 02, 2009 6:14 AM
Subject: [seqfan] Comment on A151750 [erratum]

> The problems in my original posting are somewhat harder.
> Ron Graham for example offers 1000\$ for one of them.
>
> Cheers Peter

```