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 A226776 #19 Feb 20 2014 08:55:22
%S A226776 3,4,1,7,2,1,9,2,5,1,7,3,3,1,9,0,3,7,8,2,9,4,1,4,3,0,6,2,6,5,1,1,9,9,
%T A226776 1,1,4,1,6,6,5,1,6,9,7,2,8,8,6,9,6,2,1,0,3,4,5,8,3,7,8,4,2,0,6,0,6,2,
%U A226776 6,2,8,3,7,2,6,3,8,2,4,1,5,0,3,2,9,2,8,3,4,7,8,0
%N A226776 Decimal expansion of the maximum value of f(x) = x - log(x)^log(x).
%C A226776 The value of x where f(x) is maximum is 8.06157... Note that greater precision in this value is made difficult due to a broad "flat" maximum.
%C A226776 In the recursive formula: b(n+1) = log(b(n))^log(b(n)) + c, where c is a constant, the maximum value of c, without the recursion diverging to infinity, is maximum value of the function above (3.4172192....), with b(1) set anywhere in the range 1 < b(1) <= 8.06157.
%C A226776 At values of c between 3.4172192 +/- 0.0000005 demonstrable convergence or divergence of the recursion above takes tens of thousands of iterations, increasing with further closeness to 3.4172192517331..., if b(1) is within the range above.
%C A226776 At x = e^e = 15.1542... (see A073226), the function f(x) = 0. This is the only value for b(1) where the recursion above is stable when c = 0.
%H A226776 Charles R Greathouse IV, <a href="/A226776/b226776.txt">Table of n, a(n) for n = 1..10000</a>
%e A226776 3.4172192517331903782941430626511991141665169728869621034583784206062...
%t A226776 digits = 92; FindMaximum[x-Log[x]^Log[x], {x, 3}, WorkingPrecision -> digits] // First // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Feb 20 2014 *)
%o A226776 (PARI) (x->x-log(x)^log(x))(solve(x=8,9,my(L=log(x));1-L^L*(1+log(L))/x)) \\ _Charles R Greathouse IV_, Jun 18 2013
%K A226776 nonn,cons
%O A226776 1,1
%A A226776 _Richard R. Forberg_, Jun 17 2013