Alternating Factorials

rogue · 2017-07-14, 18:41

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.

Batalov · 2017-07-14, 23:55

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

rogue · 2017-07-15, 02:28

Fixed the link. I'll let someone else sieve to the limit.

rogue · 2017-07-16, 17:58

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.

J F · 2017-07-18, 06:55

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?

rogue · 2017-07-18, 18:19

Quote:

Originally Posted by J F

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.

Batalov · 2017-07-19, 16:13

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

rogue · 2017-07-19, 16:24

Quote:

Originally Posted by Batalov

I searched a little bit with a simplistic sieve and found 43592.

Found 43592 for what?

CRGreathouse · 2017-07-19, 16:48

Quote:

Originally Posted by rogue

Found 43592 for what?

Found that A001272(24) = 43592.

rogue · 2017-07-19, 20:10

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.

ericw · 2017-08-11, 14:47

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

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 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 2017-07-30 at 03:52

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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 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 no-brainer.

2017-07-19, 16:13	#7
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 10011001100111₂ 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

2017-08-11, 14:47	#11
ericw 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