2015/05/01 by van der Kamp, Peter H
#11B37 #11B83 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1505.00194
We provide an elementary proof to a conjecture by Robinson that multiples of (powers of) primes in the Somos-4 sequence are equally spaced. We also show, almost as a corollary, for the generalised Somos-4 sequence defined by τn+2τn-2=ατn+1τn-1+βτn2 and initial values τ1=τ2=τ3=τ4=1, that the polynomial τn(α,β) is a divisor of τn+k(2n-5)(α,β) for all n,k∈\mathbb Z and establish a similar result for the generalized Somos-5 sequence.