[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
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