Consider the sequence {x_n}_(n = 0)^∞ defined by x_0 = 1 and x_(n + 1) = ⌈3/2 x_n⌉, where ⌈z⌉ is the ceiling function. For n = 0, 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 have shown that x_n satisfies x_n = ⌊K(3/2)^n⌋ for all n, where K = 1.62227... (OEIS A083286) is analogous to Mills' constant in the sense that the formula is useless unless K is known exactly ahead of time (Odlyzko and Wilf 1991, Finch 2003).

ceiling function | power floors | power fractional Parts