This paper presents new characterizations and algorithmic results for generalized Skolem and Langford sequences with minimum number of zeros. It generalize the necessary conditions for existence and locations for each zero of generalized Langford sequences. New algorithm implementations are used to find new sequences and analyze the space of solutions for a range of cases. Expanded tables of computational results are given, along with several efficient probabilistic ways of finding solutions in very large search cases.Mathematics Subject Classification: 05B