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

[Artur]

Dear Jonathan and Others,
Binary system isn't as effective as decimal because 5 or 6 last digits  
varying
%I A000001
%S A000001  
10,11,101,111,1101,10111,10101,1010011,10100011,100111101,1001110111,
10011101011,100111000111,1001110001011,10011011110101,100110111100001,
1001101110111101,10011011101010011,100110111010011101,1001101110100011111,
10011011101000111011,100110111010001101101,1001101110100010111111,
10011011101000101110101,100110111010001011010111,1001101110100010110101011,
10011011101000101101000001,100110111010001011001110011,
100110111010001011011100001,10011011101000101100110111001,
100110111010001011001101010111,1001101110100010110011010010111,
10011011101000101100110100011001,100110111010001011001101000101011,
1001101110100010110011010001000001,10011011101000101100110100001111001,
100110111010001011001101000011101111,1001101110100010110011010000110111101,
10011011101000101100110100001101011011,100110111010001011001101000011010110101
%N A000001 Biggest primes writen in binary system <2*a[n-1] a[1]=2
%C A000001 These sequence visualized Chebyshev low that between n and 2n  
existed minimum 1 prime
%F A000001 a(n) = 2*a(n-1)
%Y A000001 A006902,A040016,A120031-A120041
%O A000001 1
%K A000001 ,nonn,
%A A000001 Artur Jasinski (grafix at csl.pl), Dec 16 2006

Dnia 16-12-2006 o 18:12:23 Jonathan Post <jvospost3 at gmail.com> napisał(a):

> "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. ;)
>>
>>