OFFSET
1,3
COMMENTS
For n<16 same as A211663.
FORMULA
With the exponentiation definition E_{i=1..n} c(i) := c(1)^(c(2)^(c(3)^(...(c(n-1)^(c(n))))...))); E_{i=1..0} := 1; example: E_{i=1..4} 3 = 3^(3^(3^3)) = 3^(3^27), we get:
a(E_{i=1..n} 3) = a(E_{i=1..n-1} 3)+1, for n>=1.
G.f.: g(x)= 1/(1-x)*sum_{k=0..infinity} x^(E_{i=1..k} 3). The explicit first terms of the g.f. are
g(x)=(x+x^3+x^27+x^7625597484987+…)/(1-x).
EXAMPLE
a(n)=1, 2, 3, 4, 5 for n=1, 3, 3^3, 3^3^3, 3^3^3^3 =1, 3, 27, 7625597484987, 3^7625597484987
MATHEMATICA
Table[Length[NestWhileList[Log[3, #]&, n, #>=1&]], {n, 90}]-1 (* Harvey P. Dale, Mar 08 2020 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Hieronymus Fischer, Apr 30 2012
STATUS
approved