hihi, all - it is likely about what i wrote at the end - precision loss made my program bogus (but it was still interesting) - it seemed possible that a sufficiently slowly increasing function could get large, because then 1 + 1/f(n) is farther away from 1, so the power might be large again, but i didn't try that more later, chris On 2020-09-04 10:29, Dan Asimov wrote:
Nice analysis, George!
Yup, Hans named it — the Foias constant.
Apparently it was discovered because of a misprint in a copy of a question that originally asked whether the (much simpler) recurrence x_(n+1) = (1 + 1/x_n)^x_n (where x_1 > 0) could possibly approach oo.
—Dan
Hans Havermann wrote: ----- GH: "f(1) = 1.1874523511"
Looks like Foias' constant.
https://mathworld.wolfram.com/FoiasConstant.html -----
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