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A225059 Levels where minus signs appear in the infinite power tower representation of 2 = exp(exp(-exp(-exp(exp(-exp(exp(exp(-exp(-exp(-exp(...))))))))))). 0

%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

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Last modified June 23 21:56 EDT 2021. Contains 345402 sequences. (Running on oeis4.)