[seqfan] Re: A001370

allouche at math.jussieu.fr allouche at math.jussieu.fr
Sun Apr 21 08:00:29 CEST 2013


As far as I know this is unproven (and seemingly quite out
of reach). There was also a conjecture (that I read years
ago in a sort of French bulletin circulating among
colleagues) about integers such that s(2^n) = n,
for which the only known solution was n = 5.
This is the same as looking for k's such that
2^{s(k)} = k, whose only known solution was k = 32.

jp


Charles Greathouse <charles.greathouse at case.edu> a écrit :

> I don't think either has been proved, but 9/2*log(2)/log(10) is correct and
> e/2 is incorrect. :)
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
>
> On Sat, Apr 20, 2013 at 6:00 PM, Hans Havermann <gladhobo at teksavvy.com>wrote:
>
>> http://oeis.org/A001370
>>
>> It has been pointed out on MathFun that the comment "a(n) ~ n*e/2 where e
>> is the base of the natural logarithm 2,7182…", while not technically
>> incorrect, should in fact state: a(n) ~ n*9*log10(2)/2. It just happens
>> that 9*log10(2) is coincidentally close to e.
>>
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