[seqfan] Re: Finitude of A161620

RGWv rgwv at rgwv.com
Sat Dec 4 14:33:48 CET 2010

?Et al,

    I have extended the search (it was up to the 3049th primorial) to the 
10000th primorial for another zero. It has failed. The Mathematica coding 

k = p = 1; While[k < 10001, p = p*Prime at k; s = Floor@ Sqrt at p; If[p == s (s + 
1), Print at p]; k++ ]


-----Original Message----- 
From: Max Alekseyev
Sent: Friday, December 03, 2010 10:31 AM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: Finitude of A161620

Each zero in this sequence correspond to a value of k such that (4*k#
+ 1) is a square.
Hence, the question about the finiteness of zeros is alike Brocard's
problem which is still open:


On Thu, Dec 2, 2010 at 5:58 PM, Hans Havermann <pxp at rogers.com> wrote:
> Let f (A060797) be the floor of the square root of primorial-k (k#,
> A002110). The sequence f*(f+1)-k# for k=1,2,3,.. begins
> {0,0,0,0,42,72,0,420,6162,15560
> ,-272370,1743902,14074002,77960070
> ,-571197768
> ,-569848020,32849821160,-238745336670,247830905532,-9203096199960,..}.
> The zeros place primorial numbers in A161620 which, as far as I am
> aware, has not been proven finite. Notwithstanding the start of this
> sequence and the subsequent sign-changes, the growth of the absolute
> values of its terms seems to me quite regular and seemingly
> inexorable. Couldn't this be shaped into a proof of a finite number of
> zeros?
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