## Re: consecutive p-smooth integers

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• Is the quest for series of numbers with what essentially is the property of having extraordinarily low factors a Critical Theoretical Question, of is it in the
Message 1 of 42 , Aug 6, 2011
Is the quest for series of numbers with what essentially is the property of having extraordinarily low factors a Critical Theoretical Question, of is it in the nature of finding very interesting, dare I say "merely" very interesting, facts?

--- In primenumbers@yahoogroups.com, "Jens Kruse Andersen" <jens.k.a@...> wrote:
>
> Andrey Kulsha wrote:
> > The case of two consecutive integers was already studied
> > (Sloane's A002072, A145605), but there are little information
> > about larger chains. It there any interesting results known?
>
> There are some computational results for 3 and 4 integers in
>
> It resulted in http://oeis.org/A122464 about trios.
> Fred Schneider found:
> 1348770149848002 = 2 * 3 * 7 * 23 * 41 * 61^2 * 149 * 239 * 257
> 1348770149848001 = 19^3 * 89 * 103 * 229 * 283 * 331
> 1348770149848000 = 2^6 * 5^3 * 11 * 29 * 109 * 151 * 163 * 197
>
> --
> Jens Kruse Andersen
>
• ... Too hard! It was difficult getting just over 2 for the first time with log(287946949)/log(15823). My only consolation is that the above is also good for 15
Message 42 of 42 , Nov 8, 2011
--- In primenumbers@yahoogroups.com, Andrey Kulsha <Andrey_601@...> wrote:
>
> >> http://www.primefan.ru/stuff/math/maxs.xls
> >> http://www.primefan.ru/stuff/math/maxs_plots.gif
> >
> > Thanks, Andrey. The gradients are fanning out better now:
>
> The files were updated again.
>
> Puzzle: find a chain of 13 consecutive p-smooth integers, starting at N,
> with log(N)/log(p) greater than
>
> log(8559986129664)/log(58393) = 2.71328
>
> Best regards,
>
> Andrey
>

Too hard!

It was difficult getting just over 2 for the first time with
log(287946949)/log(15823).

My only consolation is that the above is also good for 15 consecutive 15823-smooth integers.
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