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Silverman's Sequence


Let f(1)=1, and let f(n) be the number of occurrences of n in a nondecreasing sequence of integers. then the first few values of f(n) are 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, ... (OEIS A001462). the asymptotic value of the nth term is phi^(2-phi)n^(phi-1), where phi is the golden ratio.


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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."

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Silverman's Sequence

Cite this as:

Weisstein, Eric W. "Silverman's Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SilvermansSequence.html

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