The asymptotic behavior of a family of sequences

P. Erdös; A. Hildebrand; A. Odlyzko; P. Pudaite; B. Reznick

doi:10.2140/pjm.1987.126.227

The asymptotic behavior of a family of sequences

P. Erdös, A. Hildebrand, A. Odlyzko, P. Pudaite, B. Reznick

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

A class of sequences defined by nonlinear recurrences involving the greatest integer function is studied, a typical member of the class being For this sequence, it is shown that lim a (n)/n as n → ∞ exists and equals 12/(log432). More generally, for any sequence defined by where the r_t > 0 and the m_i are integers ≥ 2, the asymptotic behavior of a(n) is determined.

Original language	English (US)
Pages (from-to)	227-241
Number of pages	15
Journal	Pacific Journal of Mathematics
Volume	126
Issue number	2
DOIs	https://doi.org/10.2140/pjm.1987.126.227
State	Published - Feb 1987
Externally published	Yes

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abstract = "A class of sequences defined by nonlinear recurrences involving the greatest integer function is studied, a typical member of the class being For this sequence, it is shown that lim a (n)/n as n → ∞ exists and equals 12/(log432). More generally, for any sequence defined by where the rt > 0 and the mi are integers ≥ 2, the asymptotic behavior of a(n) is determined.",

author = "P. Erd{\"o}s and A. Hildebrand and A. Odlyzko and P. Pudaite and B. Reznick",

year = "1987",

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AU - Hildebrand, A.

AU - Odlyzko, A.

AU - Pudaite, P.

AU - Reznick, B.

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AB - A class of sequences defined by nonlinear recurrences involving the greatest integer function is studied, a typical member of the class being For this sequence, it is shown that lim a (n)/n as n → ∞ exists and equals 12/(log432). More generally, for any sequence defined by where the rt > 0 and the mi are integers ≥ 2, the asymptotic behavior of a(n) is determined.

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