where
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)).
Odlyzko and Wilf (1991) have shown that satisfies
for all ,
where
(OEIS A083286) is analogous to Mills'
constant in the sense that the formula is useless unless is known exactly ahead of time (Odlyzko and Wilf 1991, 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.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)
![[z]](/images/equations/PowerCeilings/Inline3.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 
(OEIS A083286) is analogous to Mills'
constant in the sense that the formula is useless unless 
is known exactly ahead of time (Odlyzko and Wilf 1991, Finch
2003).
