Let 
,
and let 
be the number of occurrences of 
in a nondecreasing sequence of integers.
then the first few values of 
are 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, ... (OEIS A001462).
the asymptotic value of the 
th term is 
, where 
is the golden ratio.
Silverman's Sequence
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References
Guy, R. K. "Silverman's Sequences." §E25 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 225-226, 1994.Sloane, N. J. A. Sequence A001462/M0257 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Silverman's SequenceCite this as:
Weisstein, Eric W. "Silverman's Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SilvermansSequence.html