

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



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



