GOLOMB'S SELF-DESCRIBED SEQUENCE AND FUNCTIONAL DIFFERENTIAL EQUATIONS

摘要

A sequence (word) W of positive integers is self-described or self-generating if τ(W) = W, where τ(W) is the sequence consisting of the numbers of consecutive equal entries of W. A famous self-generating bounded sequence is Kolakoski's 1, 2, 2, 1, 1, 2, 1, 2, 2, … (see [Ch]). In this paper we consider Golomb's sequence F, which is the only nondecreasing self-generating sequence taking all positive integral values, 1, 2, 2, 3, 3, 4, 4, 4 5, 5, 5, 6, 6, 6, 6, …. Let φ denote the golden number.