2005/01/31 by Andrew N. W. Hone, Andrew Hone, Hone, Andrew
Computer Science · Mathematics · #11B37 #33E05 #37J35 #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Tensor decomposition and applications #math.NT #msc:11B37 #msc:33E05 #msc:37J35
paper · pdf · doi:10.48550/arxiv.math/0501554
More typos corrected, and extra Proposition 2.5 added. To appear in Trans. Amer. Math. Soc
openalex publication_date 2005/01/31 · arxiv created 2006/01/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Somos 5 sequences are a family of sequences defined by a fifth order bilinear recurrence relation with constant coefficients. For particular choices of coefficients and initial data, integer sequences arise. By making the connection with a second order nonlinear mapping with a first integral, we prove that the two subsequences of odd/even index terms each satisfy a Somos 4 (fourth order) recurrence. This leads directly to the explicit solution of the initial value problem for the Somos 5 sequences in terms of the Weierstrass sigma function for an associated elliptic curve.