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Old 2017-07-14, 18:41   #1
rogue
 
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Default 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
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Old 2017-07-14, 23:55   #2
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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
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Old 2017-07-15, 02:28   #3
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Fixed the link. I'll let someone else sieve to the limit.
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Old 2017-07-16, 17:58   #4
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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.
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Old 2017-07-18, 06:55   #5
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Quote:
Originally Posted by rogue View Post
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?
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Old 2017-07-18, 18:19   #6
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Quote:
Originally Posted by J F View Post
Any chance to see that in pixsieve some day?
I hadn't thought about it, but that is a possibility.

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
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Old 2017-07-19, 16:13   #7
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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
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Old 2017-07-19, 16:24   #8
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Quote:
Originally Posted by Batalov View Post
I searched a little bit with a simplistic sieve and found 43592.
Found 43592 for what?
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Old 2017-07-19, 16:48   #9
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Quote:
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Found 43592 for what?
Found that A001272(24) = 43592.
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Old 2017-07-19, 20:10   #10
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Quote:
Originally Posted by CRGreathouse View Post
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.
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Old 2017-08-11, 14:47   #11
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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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