Silverman's Sequence

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). Theasymptotic 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. SequenceA001462/M0257in ``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.

• Gauss Map
• Gauss Measure
• Gauss Multiplication Formula
• Gauss Plane
• Gauss-Salamin Formula
• Gauss's Backward Formula
• Gauss's Circle Problem
• Gauss's Class Number Conjecture
• Gauss's Class Number Problem
• Gauss's Constant
• Gauss's Criterion
• Gauss's Double Point Theorem
• Gauss's Equation (Radius Derivatives)
• Gauss's Formula
• Gauss's Formulas
• Gauss's Forward Formula
• Gauss's Harmonic Function Theorem
• Gauss's Hypergeometric Theorem
• Gauss's Inequality
• Gauss's Interpolation Formula
• Gauss's Lemma
• Gauss's Machin-Like Formula
• Gauss's Mean-Value Theorem
• Gauss's Polynomial Theorem
• Gauss's Reciprocity Theorem