Somos-4 and Somos-5 are arithmetic divisibility sequences

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 generalized Somos-4 sequence defined by tau(n+2)tau(n-2) = alpha tau(n+1)tau(n-1) + beta tau(2)(n) and initial values tau(1) = tau(2) = tau(3) = tau(4) = 1, that the polynomial tau(n)(alpha, beta) is a divisor of tau(n+k(2n-5))(alpha, beta) for all n, k is an element of Z and establish a similar result for the generalized Somos-5 sequence. The proofs involve elliptic divisibility sequences, for which we also show that primes are equally spaced, and a nice property of subsets S subset of Z for which t, s is an element of S double right arrow 2s - t is an element of S.