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Hofstadter Sequences


Let b_1=1 and b_2=2 and for n>=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, ... (OEIS A005243). Let c_1=2 and c_2=3, form all possible expressions of the form c_ic_j-1 for 1<=i<j<=n, and append them. The resulting sequence is 2, 3, 5, 9, 14, 17, 26, 27, ... (OEIS A005244).


See also

Hofstadter-Conway $10,000 Sequence, Hofstadter's Q-Sequence, Sum-Free Set

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References

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 A005244/M0705 in "The On-Line Encyclopedia of Integer Sequences."

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Hofstadter Sequences

Cite this as:

Weisstein, Eric W. "Hofstadter Sequences." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HofstadterSequences.html

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