20170316, 04:08  #1 
"Sam"
Nov 2016
117_{16} Posts 
Primes in A048788 OEIS Sequence
Is anyone able to check which indices a(n) A048788 OEIS sequence is prime for for n up to 20k or more? How can PFGW define recurrence relation nonLucas Sequences so I know how to test them? Manual primality tests yield that a(n) is prime for the following n (up to 317):
2, 3, 5, 7, 11, 13, 19, 23, 37, 43, 149, 227, 277, 311, 317 OEIS doesn't have a sequence for this, so is someone also able to verify the current results on the indices n such that a(n) is prime for. Thanks for help and feedback. More work and time also appreciated. 
20170316, 11:07  #2  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 
Quote:
Last fiddled with by science_man_88 on 20170316 at 11:12 

20170316, 20:42  #3 
Aug 2006
1011011100100_{2} Posts 
First, note that a(n) > 1 for n > 1 and that the sequence is a strong divisibility sequence, so if a(n) is prime then n is prime. So we need only check prime indices.
I added a closedform program for the sequence to make it less of a pain to work with and started crunching away. The first minute or so gave these terms: 2, 3, 5, 7, 11, 13, 19, 23, 37, 43, 149, 227, 277, 311, 317, 491, 647, 719, 947, 1039, 1193, 1499, 1867, 1933, 4591, 7127 
20170316, 20:43  #4 
Aug 2006
2^{2}·5·293 Posts 

20170316, 21:12  #5 
Aug 2006
1011011100100_{2} Posts 
A few more: 11273, 13591, 16823, 18541

20170316, 21:27  #6  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 
Quote:
https://oeis.org/A001835 all the odd placed terms. https://oeis.org/A001353 twice this one is every second of the sequence you want to talk about and these fall into a lucas sequence. Last fiddled with by science_man_88 on 20170316 at 21:53 

20170316, 23:50  #7 
"Sam"
Nov 2016
3^{2}·31 Posts 
Thanks, CRGreathouse for those terms. To make sure (so an OEIS sequence can be added), are these the correct indices n (for a(n)) in order up to n = 20k?
I will try to add in an OEIS sequence if so. Also just for curiosity, what is the density for the prime indices n such that a(n) is prime for compared to the primes n such that 2^n1 (Mersenne) is prime for? In other words, for any prime n, what is the (approximate) probability that a(n) is prime for, and for any given prime n, is there a greater chance that a(n) or 2^n1 is prime for? Last fiddled with by carpetpool on 20170316 at 23:56 
20170317, 01:32  #8  
Aug 2006
2^{2}×5×293 Posts 
Quote:
Quote:


20170317, 12:22  #9 
"Sam"
Nov 2016
3^{2}·31 Posts 
So I see you are continuing to test this sequence, or not?
I would be happy to check these terms too, though unfortunately I am stuck on defining a doublerecurrence relation with PFGW like sm88 this sequence a(n) was. If all n <= 1M were tested, these terms would be checked to 300k digits approximately? Not saying anyone should risk their computer to do all that work. (I certainly would only go to about n = 200k or 300k) which is about 60k digits. I am only making sure I got the approximations of how large these primes are. 
20170317, 22:57  #10 
Aug 2006
2^{2}×5×293 Posts 
OK, terms are
2, 3, 5, 7, 11, 13, 19, 23, 37, 43, 149, 227, 277, 311, 317, 491, 647, 719, 947, 1039, 1193, 1499, 1867, 1933, 4591, 7127, 11273, 13591, 16823, 18541, 27947, 34351, 66841, 80051, 80629, 81547 with no others through 86743. You can take it from here if you like, I'm done. The last term corresponds to a PRP23319. Through a million would be 286k digits. 
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