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A225059
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Levels where minus signs appear in the infinite power tower representation of 2 = exp(exp(-exp(-exp(exp(-exp(exp(exp(-exp(-exp(-exp(...))))))))))).
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0
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3, 4, 6, 9, 10, 11, 12, 13, 15, 18, 20, 21, 23, 25, 27, 30, 31, 32, 33, 35, 36, 38, 40, 41, 42, 43, 45, 46, 47, 48, 49, 51, 52, 54, 56, 57, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 89, 91, 92, 95, 96, 97, 100
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OFFSET
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1,1
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COMMENTS
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Start with x=2, then at every step write down the step number if x is negative, replace x with log(abs(x)), repeat.
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).
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LINKS
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EXAMPLE
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a(1)=3 because the first minus sign appears at level 3.
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MATHEMATICA
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levels = 120; Flatten[Position[Sign[NestList[Composition[Log, Abs], 2, levels]], -1]]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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