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2022-07-15, 08:38   #34
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

DF916 Posts

Quote:
 Originally Posted by charybdis Ah, yet another Sweety conjecture that's almost certainly false... Hint: do the partition numbers grow exponentially? Second hint: the probability that p(n) is prime is of order 1/sqrt(n)
Well, how about its sister sequence: “Distinct partition numbers” (https://oeis.org/A000009)?

Also other sequences like https://oeis.org/A000110, https://oeis.org/A000111, https://oeis.org/A000670, https://oeis.org/A001006?

Last fiddled with by sweety439 on 2022-07-15 at 08:38

2022-07-15, 09:23   #35
charybdis

Apr 2020

32·5·19 Posts

Quote:
 Originally Posted by sweety439 Well, how about its sister sequence: “Distinct partition numbers” (https://oeis.org/A000009)? Also other sequences like https://oeis.org/A000110, https://oeis.org/A000111, https://oeis.org/A000670, https://oeis.org/A001006?
How about you look up the asymptotics of those sequences yourself and use the Prime Number Theorem to work out whether they ought to contain infinitely many such pairs of primes?

Last fiddled with by charybdis on 2022-07-15 at 09:25

2022-07-15, 17:27   #36
frmky

Jul 2003
So Cal

246910 Posts

Quote:
 Originally Posted by Batalov look at the state of p(2335166) in FactorDb, eh? It has been proven by Greg around March, so Greg also is not a foreigner in the land of fun.
Actual credit for that goes to François Morain, but my interests are varied.

 2022-07-16, 07:01 #37 paulunderwood     Sep 2002 Database er0rr 11×389 Posts Using the following function to reverse the digits of number of partitions: Code: revnumbpart(n)=V=digits(numbpart(n));a=0;for(k=1,#V,a+=V[k]*10^(k-1));a; I get in seconds: Code: for(n=1,1000,if(ispseudoprime(revnumbpart(n)),print([n]))) [2] [3] [4] [5] [6] [9] [13] [23] [27] [34] [47] [100] [141] [185] [186] [187] [236] [241] [255] [271] [306] [310] [318] [378] [441] [481] [510] [532] [549] [661] [769] [868] [895] [931] How big a (pr)prime reversed digits number of partitions can you find? Last fiddled with by paulunderwood on 2022-07-16 at 07:07
2022-07-17, 08:07   #38
paulunderwood

Sep 2002
Database er0rr

11×389 Posts

Quote:
 Originally Posted by paulunderwood Using the following function to reverse the digits of number of partitions: Code: revnumbpart(n)=V=digits(numbpart(n));a=0;for(k=1,#V,a+=V[k]*10^(k-1));a;
I am now certifying revnumbpart(100031088) on a slow computer.

 2022-07-21, 11:51 #39 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 24·33·23 Posts p(19439060) and p(19439060)+4 are cousin primes. Work in progress: A355956 = 3, 5, 6, 13, 36, 157, 302, 546, 2502, 2732, 19439060, ...
 2022-08-02, 20:45 #40 frmky     Jul 2003 So Cal 9A516 Posts To no one's surprise, p(1000007396) is prime. Last fiddled with by frmky on 2022-08-02 at 20:45
2022-08-02, 22:59   #41
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

100110110100002 Posts

Quote:
 Originally Posted by frmky To no one's surprise, p(1000007396) is prime.
{parody of some folks' posts}
But... but.. if you sum up 1000007396's digits you will get 26.
Therefore, the digital root is 8.
If you take the digital root of p(1000007396) you will also get 8.
And if you take the digital root of numeric square root of p(1000007396) you will also get 8.
And Zawahiri's name has 8 letters.
This is not a coincidence!
There is a deep conspiracy.
{parody /} ...and half of it is not even true

2022-08-02, 23:31   #42
paulunderwood

Sep 2002
Database er0rr

427910 Posts

Quote:
 Originally Posted by frmky To no one's surprise, p(1000007396) is prime.
Nice one

2022-08-04, 01:34   #43
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

67718 Posts

Quote:
 Originally Posted by Batalov A355956 = 3, 5, 6, 13, 36, 157, 302, 546, 2502, 2732, 19439060, ...
Should this sequence be finite or infinite? (e.g. A080327 and A107360 and A120024 should be finite)

2022-08-04, 01:37   #44
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

24×33×23 Posts

Quote:
Originally Posted by sweety439
Quote:
 A355956 = 3, 5, 6, 13, 36, 157, 302, 546, 2502, 2732, 19439060, ...
Should this sequence be finite or infinite?

Maybe A355956 tells something on this subject? Ah... wait...!

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