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On Golomb's self describing sequence II

✍ Scribed by Y. -F. S. Pétermann


Book ID
105140353
Publisher
Springer
Year
1996
Tongue
English
Weight
269 KB
Volume
67
Category
Article
ISSN
0003-889X

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📜 SIMILAR VOLUMES


On Golomb′s Self Describing Sequence
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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

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Let s n = 1 + 1/2 + • • • + 1/(n -1)log n. In 1995, the author has found a series transformation of the type n k=0 μ n,k,τ s k+τ with integer coefficients μ n,k,τ , from which geometric convergence to Euler's constant γ for τ = O(n) results. In recently published papers T. Rivoal and Kh. & T. Hessam

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