EUREKA!!!!!!!!!!!!!!!!!!!!!!!!

[Jonathan Post]

"Chebychev said it and I'll say it again:
There's always a prime between n and 2n."

I skipped the attribution in A118909.*
*
Joseph Louis François Bertrand [1822-1900] was the Paris professor who made
the conjecture, proved by Chenychev in 1850. I have heard that It appears
that Nat Fine wrote this couplet in honor of Paul Erdos.

Jasinski said it, and emailed again:
There's always a prime between n and 10n.

"ten" rhymes with "n."  This is as great an advance in mathematical poetry
as any sequence containing "14" is to sonnets.  Or, more to the point, as
the fact that the number of syllables in a haiku is prime.

I'm nearly the last person to criticize anyone who submits a base sequence,
or a sequence involving primes. But when I do, I know it to be a base
sequence, and endeavor to submit the more generalized sequence of
antidiagonals of the array of such a sequence over all natural number bases.

Sometimes generalization sheds new light on a problem. Grothendieck, for
instance, as a master of that, before he turned his mind to politics. If
there is an enlightening generalization that moves beyond the arbitrariness
on decimal base, I'd be pleased to see it.

No disrespect to Jasinski.  I also have made the mistake of egotistically
proposing to name something after myself (a la Donald Trump), and over
premature exclamation marks, not symbolizing factorials, out of excitement
and enthusiam. Also, sometimes I like the sequences by this gentleman, as
indicated by A113914 and its ilk.

In this holiday season, perhaps it is best to lean towards tolerance,
charity, forgiveness, and kindness.

-- Jonathan Vos Post

On 12/16/06, Hans Havermann <pxp at rogers.com> wrote:
>
> Antti Karttunen asked:
>
> So, please tell us, what is the ground-breaking idea in your primes below?
>
>
> 17989, 179849, 1798487, 17984833, 179848309, 1798483067,
> 17984830667, 179848306667, 1798483066669, 17984830666651, 179848306666507,
> ...
>
>
> I can at least verify that:
>
> a(1) = 17989
> a(n) = PreviousPrime[10*a(n-1)]
>
> I hope there's more to it than that. ;)
>
>
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