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Basically I started with the number $15$. Then I subtracted its square root to get roughly $11.127$.

Subtracting the square root of that returned roughly $7.791$, and finally after taking the square root of that, I got roughly $5$.

According to Google, it is $5.00000861488$. It is so close to $5$ that I though it could use further investigation, but so far I haven’t found anything like it.

J. W. Tanner
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Infinite Planes
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1 Answers1

6

I don't think there is anything fundamental about this. Here's a plot of the real part for repeated applications of the process:

enter image description here

Mathematica:

iter = Re[N[NestList[(# - Sqrt[#]) &, 15, 15]]];

ListPlot[iter, Joined -> True,
 PlotRange -> {-2, 15}]
David G. Stork
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    Another piece of (fairly weak) evidence that nothing special is going on is that nothing interesting happens for other values of $15$. – Carl Schildkraut May 04 '20 at 21:12