20180919, 13:25  #12  
Feb 2017
Nowhere
2^{3}×641 Posts 
Quote:
I was unable to find a "nice" way to do this. Bruteforce checking turned up the examples already found, and showed no primes p, 3 < p < 20000 had this property for either sequence. 

20180919, 13:34  #13 
"Rashid Naimi"
Oct 2015
Remote to Here/There
87E_{16} Posts 
Not the 1st term, as nether is a(19).
Further more for a(n) = Sum_{k=0..n} k! a(0) = 1 Last fiddled with by a1call on 20180919 at 13:40 
20180919, 13:41  #14 
Jun 2003
3·11·157 Posts 
I think OFFSET 0,3 is relevant here
Last fiddled with by axn on 20180919 at 13:43 
20180919, 14:25  #15 
Aug 2006
3×1,993 Posts 
Last fiddled with by CRGreathouse on 20180919 at 14:26 
20180919, 21:19  #16 
Aug 2004
New Zealand
3^{2}×5^{2} Posts 
The sum starting from 0 is sometimes denoted !n, the sum starting from 1, K(n). See early results at http://www.asahinet.or.jp/~KC2HMSM/mathland/matha1/. I believe all those have been moved to factordb.com though.

20180919, 22:51  #17 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2×1,087 Posts 
Yes you are correct. It is relevant. It specifies the first subscript is 0 for a function that is defined to be valid for subscripts greater than or equal to 1.
Not really fixing the problem in my opinion. What is the point of including a(0) in a sequence that does not define it? How is that more significant than a(19)? 
20180920, 02:19  #18  
Aug 2006
3·1,993 Posts 
Quote:
Last fiddled with by CRGreathouse on 20180920 at 02:20 

20180920, 03:55  #19 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2×1,087 Posts 
I think this is a better reference. It much more directly explains that the concept is a convention. It is interesting that the entry does not have the usual history segment. This makes me suspect it is as new of a concept as the notion of series implying summation. That would make it younger than I am.
As of this moment Wikipedia has equivalent entries in only 15 languages. Last fiddled with by a1call on 20180920 at 04:41 
20180920, 06:44  #20 
May 2018
43 Posts 
The empty sum is equal to because in this way formulas like are correct, if . It is the only consistent way to define it.
By the way, it seems that quite a lot of effort has already been made in factoring these numbers, but there is nothing particularly interesting, it seems. 
20180920, 12:24  #21  
Aug 2006
3·1,993 Posts 
Quote:


20180920, 12:25  #22 
Aug 2006
3×1,993 Posts 

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