A071810

[franktaw at netscape.net]

I don't know for sure how he computed them, but the following works:

Compute f_n(x) = product_{k=1}^n 1+x^Prime(k) = f_{n-1}(x) * 
(1+x^Prime(n)).  Then sum the coefficients of x^p in f_n(x) for p 
prime.  You only need to look at primes <= the sum of the first n 
primes.

The hard keyword should definitely be removed.  Don, perhaps you could 
add a program as well?

Franklin T. Adams-Watters


-----Original Message-----
From: maxale at gmail.com

Don, 
 
How did you compute these values? 
If it was so easy to get them then "hard" keyword should removed from 
the sequence. 
 
Thanks, 
Max 
 
On 9/7/06, Don Reble <djr at nk.ca> wrote: 
> Franklin, seqfans: 
> 
> 1) Can anybody show that a(n+1) < 2*a(n) [for n > 1]. 
> 
> It's false: the first counterexample (after a(1) and a(2)) is 
> a(332) = 7231718580557676414340499974568912816859167222719 
> 19907962286482385524340473747270641475071066631611 
> a(333) = 14464046068617292755660165171033882640966175364732 
> 39964866791504420112662134326840615877172861788249 
> 
> I, too, suspect the limit statement, but mere computation won't 
> prove anything. 
> 
> ----- 
> 
> njas: 
> 
> I might as well fill it, eh? 
> 
> %I A071810 
> %S A071810 
1,3,5,7,12,20,35,65,122,237,448,846,1629,3157,6159,12052,23484,45731, 
> %T A071810 
89394,175742,346214,681850,1344838,2657654,5253640,10374991,20471626, 
> %U A071810 
40401929,79871387,158182899,313402605,620776215,1228390086,2430853648 
> %C A071810 a(333) > 2*a(332) -- Don Reble, Sep 07 2006 
> %E A071810 More terms from Don Reble (djr(AT)nk.ca), Sep 07 2006 
> 
> -- 
> Don Reble djr at nk.ca 
> 
> 
> -- 
> This message has been scanned for viruses and 
> dangerous content by MailScanner, and is 
> believed to be clean. 
> 
> 


________________________________________________________________________
Check Out the new free AIM(R) Mail -- 2 GB of storage and 
industry-leading spam and email virus protection.