This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A199203 #24 Oct 29 2020 15:20:09
%S A199203 4,9,8,5,6,3
%N A199203 Decimal expansion of f(0) where f is the functional square root (half-iterate) of exponent, f(f(x))=exp(x).
%C A199203 f(A199203) = 1, where f is the functional square root of exponent.
%C A199203 The listed digits are a conjecture obtained as a common result of several different numeric approximation algorithms, they haven't been rigorously proved to be correct.
%H A199203 Citizendium, <a href="http://en.citizendium.org/wiki/Superfunction">Superfunction</a>.
%H A199203 Math StackExchange, <a href="https://math.stackexchange.com/questions/2135474/half-iteration-of-exponential-function">Half iteration of exponential function</a>.
%H A199203 Gottfried Helms, <a href="http://go.helms-net.de/math/tetdocs/CoefficientsForUTetration.htm">Coefficients for fractional iterates exp(x)-1</a>.
%H A199203 Dmitry Kruchinin, Vladimir Kruchinin, <a href="http://arxiv.org/abs/1302.1986">Method for solving an iterative functional equation A^{2^n}(x)=F(x)</a>, arXiv:1302.1986 [math.CO], 2013.
%H A199203 Wikipedia, <a href="https://en.wikipedia.org/wiki/Functional_square_root">Functional square root</a>.
%e A199203 0.498563...
%t A199203 n = 23; p[s_, 1] := c[s]; p[0, n_] := c[0]^n; p[s_, n_] := p[s, n] = Expand[Sum[c[k] p[s - k, n - 1], {k, 0, s}]]; d[n_, 0] := Sum[c[k] c[0]^k, {k, 0, n}]; d[n_, i_] := Sum[c[k] p[i, k], {k, 1, n}]; a = c[0] /. FindRoot[Table[d[n, k] k! == 1, {k, 0, n}], Table[{c[k], 2^-k}, {k, 0, n}], WorkingPrecision -> 30]; First[RealDigits[a, 10, 6]]
%Y A199203 Cf. A001113, A184011.
%K A199203 nonn,cons,more,hard
%O A199203 0,1
%A A199203 _Vladimir Reshetnikov_, Nov 03 2011