A note on Buell’s Theorem on length four Büchi sequences
Résumé
Büchi sequences are sequences whose second difference of squares is the sequence (2,..., 2), like for instance (6, 23, 32, 39) – so they can be seen as a generalization of arithmetic progressions. No (non-trivial) length 5 Büchi sequence is known to exist. Length four Büchi sequences were parameterized by D. A. Buell in 1987. We revisit his theorem, fixing the statement (about 26% of the Büchi sequences from R. G. E. Pinch's 1993 table were missed), and giving a much simpler proof.
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