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The constant is exactly $\sum_{n=1}^∞\frac{1}{n^n}$. Why does it seem that no one has written about it? Did I not search well enough? If so, what is the name for it? If not, it is not sufficiently "interesting?" I can't find it anywhere, which seems very strange.

(I apologize about how little my experience in higher maths I have...)

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closed as unclear what you're asking by user223391, Adam Hughes, JonMark Perry, Marc van Leeuwen, SchrodingersCat Jun 1 '16 at 9:28

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    $\begingroup$ See the sophomore's dream $\endgroup$ – Omnomnomnom May 31 '16 at 21:04
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    $\begingroup$ @MiloBrandt: yes it is. Due to Lagrange inversion theorem, such a constant is related with the Lambert function. If such a constant were rational, it would give $e^a=b$ with $a,b\in\mathbb{Q}$. That may happen only at $a=0$ since $e$ is a trascendental number. $\endgroup$ – Jack D'Aurizio May 31 '16 at 21:04
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    $\begingroup$ The OEIS has a page about it: oeis.org/A073009. You can find it by typing in the digits 1, 2, 9, 1, 2, 8 into the search bar. Also see the references in the "Links" section on that page. $\endgroup$ – Rahul May 31 '16 at 21:06
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    $\begingroup$ But obviously its "weirdness" is not enough to prove its irrationality. $\endgroup$ – Jack D'Aurizio May 31 '16 at 21:06
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    $\begingroup$ @asherdrummond Erm... how do you do the logical jump between the first and second part of your sentence? $\endgroup$ – Clement C. May 31 '16 at 21:24
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What? You mean the Sophomore's Dream? (Actually, the "dream" is that $\int_0^1 x^{-x} \,\mathrm{d}x = \sum_{n=1}^\infty n^{-n}$, but this is just two representations of your value.)

Your value appears in the ISC, associated with that sum.

This sequence of digits appears in the OEIS as A073009 (with various references, including to Bernoulli's proof that the integral equals the sum).

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    $\begingroup$ Why do you think it has "a name" other than "the constant $\sum_{n=1}^\infty n^{-n}$"? That's a short and unambiguous identifier. $\endgroup$ – Eric Towers May 31 '16 at 23:19
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    $\begingroup$ Are you sure about that? Do you know anything about my browser? Let me introduce you to lynx. $\endgroup$ – Eric Towers May 31 '16 at 23:31
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    $\begingroup$ I've been reading it and writing it for a few years. It's not quite automatic when running into someone else's spacing patterns, but I read mine pretty much fluently. Also, there is no hope of MathJax rendering in a non-graphical or non-Javascript browser (or browser that has had those turned off). $\endgroup$ – Eric Towers May 31 '16 at 23:41
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    $\begingroup$ @EricTowers: I'm surprised lynx can run all the javascript used by Math SE. If I disable it I can log in but can't view or post comments. $\endgroup$ – user21820 Jun 1 '16 at 5:18
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    $\begingroup$ @asherdrummond Wow intending to improve on Knuth's (and a couple thousand volunteers work) is certainly a stretch goal. $\endgroup$ – DRF Jun 1 '16 at 9:33

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