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Old 2022-07-15, 08:38   #34
sweety439
 
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Quote:
Originally Posted by charybdis View Post
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
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Old 2022-07-15, 09:23   #35
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Quote:
Originally Posted by sweety439 View Post
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
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Old 2022-07-15, 17:27   #36
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Quote:
Originally Posted by Batalov View Post
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.
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Old 2022-07-16, 07:01   #37
paulunderwood
 
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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
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Old 2022-07-17, 08:07   #38
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Quote:
Originally Posted by paulunderwood View Post
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.
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Old 2022-07-21, 11:51   #39
Batalov
 
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p(19439060) and p(19439060)+4 are cousin primes.

Work in progress: A355956 = 3, 5, 6, 13, 36, 157, 302, 546, 2502, 2732, 19439060, ...
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Old 2022-08-02, 20:45   #40
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To no one's surprise, p(1000007396) is prime.

Last fiddled with by frmky on 2022-08-02 at 20:45
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Old 2022-08-02, 22:59   #41
Batalov
 
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Quote:
Originally Posted by frmky View Post
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
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Old 2022-08-02, 23:31   #42
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Quote:
Originally Posted by frmky View Post
To no one's surprise, p(1000007396) is prime.
Nice one
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Old 2022-08-04, 01:34   #43
sweety439
 
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Quote:
Originally Posted by Batalov View Post
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)
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Old 2022-08-04, 01:37   #44
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Quote:
Originally Posted by sweety439 View Post
Quote:
A355956 = 3, 5, 6, 13, 36, 157, 302, 546, 2502, 2732, 19439060, ...
Should this sequence be finite or infinite?
I have concerns about your reading comprehension.

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