%I
%S 3,4,6,9,10,11,12,13,15,18,20,21,23,25,27,30,31,32,33,35,36,38,40,41,
%T 42,43,45,46,47,48,49,51,52,54,56,57,59,61,62,63,65,66,67,69,70,71,72,
%U 73,74,76,77,78,79,80,81,82,83,85,86,89,91,92,95,96,97,100
%N Levels where minus signs appear in the infinite power tower representation of 2 = exp(exp(exp(exp(exp(exp(exp(exp(exp(exp(exp(...))))))))))).
%C Start with x=2, then at every step write down the step number if x is negative, replace x with log(abs(x)), repeat.
%C 2 = exp(exp(exp(exp(exp(exp(exp(exp(exp(exp(exp(...))))))))))) in the sense that 2 is the limit of the sequence of power towers with increasing heights generated from initial segments of this sequence: exp(1), exp(exp(1)), exp(exp(exp(1))), exp(exp(exp(exp(1)))), exp(exp(exp(exp(exp(1))))), ... (the initial seed value here is taken to be 1, but it can be any number as the limit does not depend on it).
%e a(1)=3 because the first minus sign appears at level 3.
%t levels = 120; Flatten[Position[Sign[NestList[Composition[Log, Abs], 2, levels]], 1]]
%K nonn,easy
%O 1,1
%A _Vladimir Reshetnikov_, Apr 26 2013
