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(...))))))))))).

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

Offset

1,1

Comments

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).

Links

Table of n, a(n) for n=1..66.

Example

a(1)=3 because the first minus sign appears at level 3.

Mathematica

levels = 120; Flatten[Position[Sign[NestList[Composition[Log, Abs], 2, levels]], -1]]

Crossrefs

Sequence in context: A284615 A186709 A143037 * A190899 A173671 A325440

Adjacent sequences: A225056 A225057 A225058 * A225060 A225061 A225062

Keyword

nonn,easy

Author

Vladimir Reshetnikov, Apr 26 2013

Status

approved