# [seqfan] Re: new sequences needing more terms

Neil Sloane njasloane at gmail.com
Fri Jun 1 22:01:26 CEST 2012

```I gave it a better name: a(n) = 1 + integer log of n (cf. A001414). It's
certainly not
my sequence! I also added more references.

On Fri, Jun 1, 2012 at 3:37 PM, Alonso Del Arte <alonso.delarte at gmail.com>wrote:

> 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.
> >
> >
> > ______________________________**_________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
>
>
> --
> Alonso del Arte
> Author at SmashWords.com<
> https://www.smashwords.com/profile/view/AlonsoDelarte>
> Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

--
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA