for all nonnegative integers, where is the floor function
and
(OEIS A083286) is analogous to Mills'
constant. A finite prefix requires only sufficiently accurate bounds on . The formula
does not by itself simplify the computation because the known method of computing
uses the sequence
itself (Odlyzko and Wilf 1991, p. 239; Finch 2003).
Finch, S. R. "Powers of 3/2 Modulo One." §2.30.1 in Mathematical
Constants. Cambridge, England: Cambridge University Press, pp. 194-199,
2003.Odlyzko, A. M. and Wilf, H. S. "Functional Iteration
and the Josephus Problem." Glasgow Math. J.33, 235-240, 1991.
https://doi.org/10.1017/S0017089500008272.Sloane,
N. J. A. Sequences A061419 and A083286 in "The On-Line Encyclopedia of Integer
Sequences."Wolfram, S. A
New Kind of Science. Champaign, IL: Wolfram Media, p. 100,
2002.
defined by 
and
![x_(n+1)=[3/2x_n]](/images/equations/PowerCeilings/NumberedEquation1.svg)
, where ![[z]](/images/equations/PowerCeilings/Inline4.svg)
is the ceiling function.
For 
,
1, ..., the first few terms are 1, 2, 3, 5, 8, 12, 18, 27, 41, 62, ... (OEIS A061419;
Wolfram 2002, p. 100,
Fig. (b)).
satisfies
, where 
is the floor function
and 
(OEIS A083286) is analogous to Mills'
constant. A finite prefix requires only sufficiently accurate bounds on 
. The formula
does not by itself simplify the computation because the known method of computing
uses the sequence
itself (Odlyzko and Wilf 1991, p. 239; Finch 2003).
