20170714, 18:41  #1 
"Mark"
Apr 2003
Between here and the
2·3,301 Posts 
Alternating Factorials
I've decided to extend this OEIS sequence, which is also known as an Alternating Factorial. I wrote a custom sieve and a pfgw script to process the output file from the sieve. I intend to sieve and test to n = 100000. Like factorials, this form removes a smaller percentage of candidates than other forms. I have sieved to 4e10 and 44% of the original terms still remain. Sieving at this time has a removal rate of about onefifth what it needs to be in order to sieve to an appropriate depth.
My program can be easily modified to support this sequence, also known as a Factorial Sum. If anyone is interested in taking on such a search, please let me know and I'll cook up some software for you. Last fiddled with by rogue on 20170715 at 02:27 
20170714, 23:55  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3·29·113 Posts 
You must have meant A001272 not A005165.
The beauty of this sequence is that it has the maximum. (because it is finite) If you sieve up to n=3612701 (instead of 100,000) then you "will sieve them all"! All of similar sequences are likely to be finite. For example: A063833 :: !n  3 is prime; it is finite (and complete in its present form) because for all n >= 467, 467  !n  3. Extensions: A001272(24) = 43592, Jul 19 2017 A100614(20) = 41532, Jul 22 2017 A100289(19) = 32841, Jul 29 2017 Last fiddled with by Batalov on 20170730 at 03:52 
20170715, 02:28  #3 
"Mark"
Apr 2003
Between here and the
2·3,301 Posts 
Fixed the link. I'll let someone else sieve to the limit.

20170716, 17:58  #4 
"Mark"
Apr 2003
Between here and the
2×3,301 Posts 
I wrote an OpenCL version of the sieving code. It is 20x faster than the assembler code in my other sieve. That makes the decision to switch a nobrainer.

20170718, 06:55  #5 
Sep 2013
2^{3}×7 Posts 

20170718, 18:19  #6 
"Mark"
Apr 2003
Between here and the
2·3,301 Posts 
I hadn't thought about it, but that is a possibility.
BTW, due to differences in how the sieves work, the nonGPU code is slower with smaller p than the GPU code. The actual rate is about 12x faster. Last fiddled with by rogue on 20170718 at 18:20 
20170719, 16:13  #7 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10011001100111_{2} Posts 
I searched a little bit with a simplistic sieve and found 43592.
I am now searching for the extension of the halfleftfactorials: http://oeis.org/A100614 
20170719, 16:24  #8 
"Mark"
Apr 2003
Between here and the
2·3,301 Posts 

20170811, 14:47  #11 
Oct 2015
19 Posts 
https://oeis.org/A100289
Numbers n such that (1!)^2 + (2!)^2 + (3!)^2 +...+ (n!)^2 is prime. a(19) = 32841 from Serge Batalov, Jul 29 2017 
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