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Suite auto-décrite de Golomb et équations fonctionnelles associées

Abstract : In this thesis, we study the asymptotic bahavior of Golomb's sequence u={1,2,2,3,3,4,4,4,5,5,5,6,6,6,6,...}, which is the only non-decreasing sequence of integers with u(1)=1 and where u(n) is the number of occurences of n in the sequence u={u(1),u(2),...}. We prove that each solution of the differential equation f'(x)=1/f(f(x)) admits an asymptotic development and we obtain relations between it's coefficients. We compare Golomb'sequence to one of these solutions and we prove that Golomb's sequence admits such an asymptotic development too.
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https://hal.univ-lorraine.fr/tel-01748112
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Submitted on : Thursday, March 29, 2018 - 11:25:20 AM
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  • HAL Id : tel-01748112, version 1

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Olivier Binda. Suite auto-décrite de Golomb et équations fonctionnelles associées. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2004. Français. ⟨NNT : 2004NAN10167⟩. ⟨tel-01748112⟩

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