Conversational question generation is a novel area of NLP research which has a range of potential applications. This paper is first to present a framework for conversational question generation that is unaware of the corresponding answers. To properly generate a question coherent to the grounding text and the current conversation history, the proposed framework first locates the focus of a question in the text passage, and then identifies the question pattern that leads the sequential generation of the words in a question. The experiments using the CoQA dataset demonstrate that the quality of generated questions greatly improves if the question foci and the question patterns are correctly identified. In addition, it was shown that the question foci, even estimated with a reasonable accuracy, could contribute to the quality improvement. These results established that our research direction may be promising, but at the same time revealed that the identification of question patterns is a challenging issue, and it has to be largely refined to achieve a better quality in the end-to-end automatic question generation.