[seqfan] Re: A045575

[Tom Duff]

And, that's not true either. I hope this Diet Coke works before coach
benches me.

On Mon, Jun 12, 2023 at 11:07 AM Tom Duff <eigenvectors at gmail.com> wrote:

> Duh, the log base doesn't matter. Same results regardless of which one you
> pick. I'll go looking for caffeine now.
>
> On Mon, Jun 12, 2023 at 10:55 AM Tom Duff <eigenvectors at gmail.com> wrote:
>
>> Wrong. (I blame early rising and insufficient caffeine.)
>> 133396671.06 is what you get for
>> 0.5*log2(10^60000)^2/ln(log2(10^10000))^2.
>> It's just weird that it's close to the right number.
>>
>> On Mon, Jun 12, 2023 at 10:45 AM Tom Duff <eigenvectors at gmail.com> wrote:
>>
>>> If you take logs base 2 rather than natural logs, you get 133396671.06.
>>> Maybe that's what Pillai meant.
>>>
>>> On Mon, Jun 12, 2023 at 10:40 AM Hans Havermann <gladhobo at bell.net>
>>> wrote:
>>>
>>>> https://oeis.org/A045575
>>>>
>>>> A Charles Greathouse comment says: "Pillai proved that there are ~ 0.5
>>>> * (log x)^2/(log log x)^2 members of this sequence up to x."
>>>>
>>>> I recently calculated that there are 133090654 terms of this sequence
>>>> less than 10^60000. The above Pillai formula suggests 6.81215*10^7, unless
>>>> I miscalculated. I contacted Greathouse about this via OeisWiki one week
>>>> ago but have not received a response. The Waldschmidt link mentioning
>>>> Pillai appears to be about solutions of Diophantine inequalities but I'm
>>>> having difficulty understanding how it relates to A045575. Perhaps someone
>>>> here with a better grasp of mathematics than I can have a look.
>>>>
>>>> --
>>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>>
>>>