%I
%S 1,74,164,4822,16609,743325,1640565,45332594
%N Least number k such that (1+1/k)^k yields n digits of e (A001113).
%e a(1) = 1 because (1+1/1)^1= 2 which equals e in the units place.
%e a(2) = 74 because (1+1/73)^73 = 2.69989... but (1+1/74)^74 = 2.700139...; thus 74 is the least number which will give e to 2 place accuracy, namely 2.7.
%t f[0] = 0; f[n_] := f[n] = Block[{k = f[n  1] + 1, d = FromDigits[{Take[ RealDigits[E, 10, 111][[1]], n], 1}]}, While[(1 + 1/k)^k < d, k++ ]; k]; Table[ f[n], {n, 6}]
%Y Cf. A001113.
%K nonn,base
%O 1,2
%A _Robert G. Wilson v_, Apr 02 2005
