Hooked k-extended skolem sequences

A hooked k-extended Skolem sequence of order n is a sequence s(1)s(2)...s(2n+2) in which s(k) = s(2n+1) = epsilon (epsilon is the null symbol) and each j is an element of{1, 2,..., n} occurs exactly twice, the two occurrences separated by exactly j - 1 symbols. It is proved that, with the exception of (k, n) = (2, 1), such a sequence exists if and only if n = 0, 1 (mod 4) for k even, and n = 2, 3 (mod 4) for k odd. This result is then used to give an alternative proof of the existence of bicyclic Steiner triple systems. (C) 1999 Elsevier Science B.V. All rights reserved.