[seqfan] Re: A214089

[Neil Sloane]

The sequence derived from A118478 now has an entry of its own - it is
A215021. It is certainly different from your sequence, which should
probably also have its own entry - I suggest you submit it!
Neil

On Tue, Jul 31, 2012 at 2:03 PM, Jonathan Stauduhar <jstdhr at gmail.com>wrote:

> Howdy,
>
> I observed that for the first 14 terms in A214089 <
> https://oeis.org/A214089> , the following holds:
>
>   p^2 - 1 / n# = 4x.
>
> In other words, p^2 - 1 / n# is congruent to 0 MOD 4.
>
> Subsequent to this observation , two new terms were added and the above
> holds true for those as well.
>
> Solving for x gives the sequence {1, 1, 1, 1, 19, 17, 1, 2567, 3350,
> 128928, 3706896, 1290179, 100170428, 39080794, 61998759572, 7833495265}.
>
> Can someone far more familiar with prime numbers explain why this may or
> may not be true for all a(n)?  I would like to add a comment to the
> sequence noting this observation, but I am unsure whether it is in fact
> true for all a(n).
>
>  I don't know if this is relevant, but I found a comment, by Robert G.
> Wilson, in A118478 <https://oeis.org/A118478> which defines another
> sequence whose first seven terms are {1, 1, 1, 1, 19, 17, 1} and also has
> 39080794 as its 14th term.
>
> -Jonathan
>
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-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
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