[seqfan] Re: new sequences needing more terms
Alonso Del Arte
alonso.delarte at gmail.com
Fri Jun 1 21:37:51 CEST 2012
It would also be nice for A036288 to have some kind of name. To get the
ball rolling on suggestions, I suggest: "Sloane's factorization twist
function"
Al
On Fri, Jun 1, 2012 at 2:49 PM, Hans Havermann <gladhobo at teksavvy.com>wrote:
> A212814
> a(n) = number of integers k >= 7 such that A212813(k) = n.
> 1, 3, 11, 2632
>
> I wrote:
>
> Assuming that a(5) is indeed the sum of the number of prime partitions of
>> the 2632 numbers in a(4) doesn't just imply that "the next term may be very
>> large" (as Neil comments) but that a(5) is essentially incalculable, since
>> it would include the number of prime partitions of 2*3^86093441-1. Is there
>> even a way to approximate this?
>>
>
> I found my message to this list in the comment section of A212814, to
> which Neil added that there is an asymptotic formula for the sum of the
> number of prime partitions (which answers the "is there a way to
> approximate this" part of my query).
>
> Unfortunately, having mistaken the offset in A212815, my use of
> 2*3^86093441-1 was in error. To calculate a(5) of A212814 using my "sum of
> the number of prime partitions of one less than each of the 2632 numbers in
> a(4)" assumption, one need only calculate the exact number of prime
> partitions of numbers up to 258280325. Having actually calculated these for
> numbers up to 50000 (a couple of years ago), I'm aware of the difficulty of
> the process. Scaling those results into the millions is not something that
> I could do on my antiquated hardware. Nonetheless, the much-smaller number
> places the notion of a(5) being "essentially incalculable" into one of
> "essentially do-able".
>
> I'm going to edit/delete the latter part of the comment in A212814 to
> remove my mistake.
>
>
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Alonso del Arte
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