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 2017-07-14, 18:41 #1 rogue     "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 one-fifth 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 2017-07-15 at 02:27
 2017-07-14, 23:55 #2 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 266716 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 2017-07-30 at 03:52
 2017-07-15, 02:28 #3 rogue     "Mark" Apr 2003 Between here and the 2·3,301 Posts Fixed the link. I'll let someone else sieve to the limit.
 2017-07-16, 17:58 #4 rogue     "Mark" Apr 2003 Between here and the 147128 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 no-brainer.
2017-07-18, 06:55   #5
J F

Sep 2013

23×7 Posts

Quote:
 Originally Posted by rogue I wrote an OpenCL version of the sieving code. It is 20x faster than the assembler code in my other sieve.
Any chance to see that in pixsieve some day?

2017-07-18, 18:19   #6
rogue

"Mark"
Apr 2003
Between here and the

2×3,301 Posts

Quote:
 Originally Posted by J F Any chance to see that in pixsieve some day?

BTW, due to differences in how the sieves work, the non-GPU code is slower with smaller p than the GPU code. The actual rate is about 12x faster.

Last fiddled with by rogue on 2017-07-18 at 18:20

 2017-07-19, 16:13 #7 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 266716 Posts I searched a little bit with a simplistic sieve and found 43592. I am now searching for the extension of the half-left-factorials: http://oeis.org/A100614
2017-07-19, 16:24   #8
rogue

"Mark"
Apr 2003
Between here and the

2×3,301 Posts

Quote:
 Originally Posted by Batalov I searched a little bit with a simplistic sieve and found 43592.
Found 43592 for what?

2017-07-19, 16:48   #9
CRGreathouse

Aug 2006

3·1,993 Posts

Quote:
 Originally Posted by rogue Found 43592 for what?
Found that A001272(24) = 43592.

2017-07-19, 20:10   #10
rogue

"Mark"
Apr 2003
Between here and the

2×3,301 Posts

Quote:
 Originally Posted by CRGreathouse Found that A001272(24) = 43592.
I'm surprised that you poached something I was working on. BTW, I'm still sieving, so I won't do PRP testing until adequately sieved.

 2017-08-11, 14:47 #11 ericw     Oct 2015 238 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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