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A088527
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Define a Fibonacci-type sequence to be one of the form s(1) = s_1 >= 1, s(2) = s_2 >= 1, s(n+2) = s(n+1) + s(n); then a(n) = maximal m such that n is the m-th term in some Fibonacci-type sequence.
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1
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2, 3, 4, 4, 5, 4, 5, 6, 5, 5, 6, 5, 7, 6, 5, 6, 6, 7, 6, 6, 8, 6, 7, 6, 6, 7, 6, 7, 8, 6, 7, 6, 7, 9, 6, 7, 8, 7, 7, 6, 7, 8, 7, 7, 8, 7, 9, 7, 7, 8, 7, 7, 8, 7, 10, 7, 7, 8, 7, 9, 8, 7, 8, 7, 7, 8, 7, 9, 8, 7, 8, 7, 9, 8, 7, 10, 8, 7, 8, 7, 9, 8, 7, 8, 8, 9, 8, 7, 11
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The m-th term in a Fibonacci-type sequence is smallest for the Fibonacci sequence itself. a(Fibonacci(n)) = n (which corresponds to taking s_1 = s_2 = 1). This gives an upper bound a(t) <= log_phi(sqrt(5)*t), roughly. Denes asks: How small can a(n) be and when do small values occur?
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REFERENCES
| T. Denes, Problem 413, Discrete Math. 272 (2003), 302 (but there are several errors in the table given there).
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CROSSREFS
| See A088858 for another version.
Sequence in context: A036370 A005208 A110007 * A030602 A133947 A060197
Adjacent sequences: A088524 A088525 A088526 * A088528 A088529 A088530
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 20 2003
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EXTENSIONS
| Corrected and extended by Don Reble (djr(AT)nk.ca), Nov 21 2003
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