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Hofstadter Sequences

Let $b_1=1$ and $b_2=2$ and for $n\geq 3$, let $b_n$ be the least Integer $>b_{n-1}$ which can be expressed as the Sum of two or more consecutive terms. The resulting sequence is 1, 2, 3, 5, 6, 8, 10, 11, 14, 16, ... (Sloane's A005243). Let $c_1=2$ and $c_2=3$, form all possible expressions of the form $c_ic_j-1$ for $1\leq i<j\leq n$, and append them. The resulting sequence is 2, 3, 5, 9, 14, 17, 26, 27, ... (Sloane's A005244).

See also Hofstadter-Conway $10,000 Sequence, Hofstadter's Q-Sequence


Guy, R. K. ``Three Sequences of Hofstadter.'' §E31 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 231-232, 1994.

Sloane, N. J. A. Sequences A005243/M0623 and A00524/M0705 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein