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Old 2022-08-04, 01:52   #45
sweety439
 
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Quote:
Originally Posted by Batalov View Post
I have concerns about your reading comprehension.

Maybe A355956 tells something on this subject? Ah... wait...!
Well, I saw the OEIS page, this sequence should be infinite, but is 157 the largest odd term?
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Old 2022-08-04, 01:52   #46
charybdis
 
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Quote:
Originally Posted by Batalov View Post
Maybe A355956 tells something on this subject? Ah... wait...!
I'm not sure whether to laugh or cry... you submit several new OEIS sequences, put "this sequence should be infinite" comments on all of them solely to make Sweety's life easier, and then this happens...
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Old 2022-08-04, 02:04   #47
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Quote:
Originally Posted by sweety439 View Post
Well, I saw the OEIS page, this sequence should be infinite
Then why did you ask whether it was finite or infinite?

Quote:
but is 157 the largest odd term?
What do you think is more likely?

1. There is some as-yet-undiscovered property of p(n) for n odd that makes it much, much less likely to be part of a cousin prime pair than a random number of the same size would be.
2. Those 5 consecutive even terms are a coincidence.
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Old 2022-08-04, 02:49   #48
sweety439
 
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Quote:
Originally Posted by charybdis View Post
Then why did you ask whether it was finite or infinite?



What do you think is more likely?

1. There is some as-yet-undiscovered property of p(n) for n odd that makes it much, much less likely to be part of a cousin prime pair than a random number of the same size would be.
2. Those 5 consecutive even terms are a coincidence.
Well ....

There is no single known odd composite term, and there is no single known term > 3 which is == 3 mod 4

Last fiddled with by sweety439 on 2022-08-04 at 02:49
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Old 2022-08-04, 11:50   #49
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Quote:
Originally Posted by sweety439 View Post
Well ....

There is no single known odd composite term, and there is no single known term > 3 which is == 3 mod 4
And there is a grand total of how many known terms? Eleven.

But - the index suddenly jumps from 2732 to 19439060 - surely there must be something going on! Argle bargle! Argle bargle!

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Old 2022-08-04, 12:08   #50
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Quote:
Originally Posted by sweety439 View Post
Well ....

There is no single known odd composite term, and there is no single known term > 3 which is == 3 mod 4
The indices of the first 17 partition primes are 2, 3, 4, 5, 6, 13, 36, 77, 132, 157, 168, 186, 188, 212, 216, 302, 366...

I'm sure that if we were in the 1950s and this was the full known extent of the sequence, you'd have been speculating that there are no more odd terms.

When the next term was discovered to be 417, you'd have said that maybe there are no terms that are 3 mod 4 apart from 3. And then it turns out 491 is in the sequence.

It's easy to go looking for patterns. But if it's not outrageously unlikely for them to have appeared by chance, and there's no good reason for them to exist, you shouldn't expect them to continue forever.
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