Silverman's sequence is the nondecreasing sequence of positive
integers with
in which each positive integer occurs exactly times. The first few terms are 1, 2, 2, 3, 3, 4, 4, 4,
5, 5, 5, ... (OEIS A001462).
The asymptotic behavior is as (Pétermann et al. 1999, p. 212),
where
is the golden ratio.
Guy, R. K. "Silverman's Sequences." §E25 in Unsolved
Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 225-226,
1994.Pétermann, Y.-F. S.; Rémy, J.-L.; and Vardi,
I. "On a Functional-Differential Equation Related to Golomb's Self-Described
Sequence." J. Théor. Nombres Bordeaux11, 211-230, 1999.
https://doi.org/10.5802/jtnb.247.Sloane,
N. J. A. Sequence A001462/M0257
in "The On-Line Encyclopedia of Integer Sequences."
of positive
integers with 
in which each positive integer 
occurs exactly 
times. The first few terms are 1, 2, 2, 3, 3, 4, 4, 4,
5, 5, 5, ... (OEIS A001462).
as 
(Pétermann et al. 1999, p. 212),
where 
is the golden ratio.
