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%I #12 Jan 17 2018 17:49:45
%S 9,9,1,9,9,1,9,9,9,7,9,8,9,9,9,3,7,9,9,1,1,9,9,3,2,9,9,2,9,9,9,1,9,9,
%T 9,1,5,9,9,1,1,9,9,9,9,9,9,1,4,9,9,1,6,9,9,1,7,9,9,1,1,9,9,1,3,9,9,1,
%U 5,9,9,1,9,9,9,1,1,9,9,6,9,9,9,1,9,9,9,4,4,9,9,1,8,9,9,1,1,9,9,1,2,9,9,2,9
%N Decimal expansion of the largest arbitrarily-long Type-2 Trott-like constant (see A178160 for definition).
%C For n=1,2,..., the largest n-digit numbers in A178160 are 9, 99, 991, 9919, etc., so a(1)=9, a(2)=9, a(3)=1, a(4)=9, etc.
%C The number of digits of agreement increases as more digits are used, but the ratio (digits of agreement divided by digits used) is between 0.31 and 0.32 when the number of digits used is between a few hundred and a few thousand; this rate of convergence is not nearly as good as that of the second Trott constant (A091694).
%H Jon E. Schoenfield, <a href="/A178164/b178164.txt">Table of n, a(n) for n = 0..3999</a>
%e 0+9/(9+1/(9+9/(1+9/(9+9/(7+9/(8+9/(9+9/(3+7/(9+9/...))))))))) = 0.9919919997989993799...
%Y Cf. A091694, A113307, A178160.
%K nonn,cons
%O 0,1
%A _Jon E. Schoenfield_, May 21 2010
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