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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, ... (Sloane's A001462). The
asymptotic value of the
th term is
, where
is the Golden Ratio.
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 ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.