I have been looking for the first appearance of the Conway base 13 function in the literature, but the only thing I have found is the wikipedia article whose unique element in the bibliography I cannot find in the given place. And after searching, I have not found any clue in the Internet about its first appearance or original article. Any help?
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As Craig said you could email him or talk to him at this summer school this very summer.
A colleague of mine at my faculty, Jon Asier Bárcena, attended to Modern Mathematics- International Summer School for Students. There he was able to talk directly to John H. Conway, and according to him, Conway said that it was developed during his teaching activity while he was planting questions to his students in a course. So apparently, the primary source is a lecture from him.