On Golombβ²s Self Describing Sequence
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Y.F.S. Petermann
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Article
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1995
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Elsevier Science
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English
β 280 KB
A proof of the oscillation estimate \(E(n)=\Omega_{ \pm}\left(n^{\phi-1-c}\right)\) is given, where \(E(n):=\) \(F(n)-\phi^{2-\phi} n^{\phi-1}\) and \(F\) is the nondecreasing "self describing" sequence \(1,2,2,3,3\), 4. 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9... defined by \(F(1)=1\) a