Re: consecutive p-smooth integers
- --- In email@example.com, "djbroadhurst"
> Definition: A sequence of consecutive positiveMy current record is s = 4.1067361598, achieved with
> integers, beginning with N, has strength
> s = log(N)/log(p), where p is the largest prime
> dividing any integer in the sequence.
> Puzzle: Find a sequence of 5 consecutive integers with
> strength s > 3.80.
> I imagine that Jens might soon beat strength s = 4.009147298.
x = 20375617
N = (x^2-3^4)*(x^2-2^10)/55440 = 3108993777544846030873003
- --- In firstname.lastname@example.org, 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,
It was difficult getting just over 2 for the first time with
My only consolation is that the above is also good for 15 consecutive 15823-smooth integers.